1: The principle that all microscopic physical entities have both wave and particle properties is called the wave-particle
a. Singularity
b. Duality
c. Triality
d. Infinality
2: The full Schrodinger’s equation in compact form is
a. $\mathbf{H\mathrm{\Psi}=i\hbar\frac{\partial\Psi\ \ }{\partial t}}$
b. $H\mathrm{\Psi}\ =\hbar\frac{\partial\Psi}{\partial t}$
c. $H\mathrm{\Psi}\ =\ i\frac{\partial\Psi}{\partial t}$
d. $H\mathrm{\Psi}\ =\ i\hbar\frac{\partial\Psi}{\partial x}$
3: In the probabilistic interpretation of wave function ![]()
, the quantity is
a. Probability density
b. Probability amplitude
c. Negative probability
d. 1
4: The probability of finding a particle in differential region dx is
a. $\mathrm{\Psi}(x,\ t)dx$
b. $\mathrm{\Psi}\left(x,t\right)^\ast dx$
c. $[\mathrm{\Psi}\left(x,t\right)^\ast/\mathrm{\Psi}(x,t)] dx$
d. $\mathbf{\Psi\left(x,t\right)^\ast\Psi(x,\ t)dx}$
5: A physical requirement on wavefunctions is that they should be
a. Reliable
b. Square integrable
c. Zero
d. Discrete
6: The charge on an electron is represented by e. Which of the following charges can exist
a. 2.0 e
b. 2.5 e
c. 3.6 e
d. 5.2 e
7: The energy of a photon depends on its
a. Amplitude
b. Speed
c. Temperature
d. Pressure
8: When an electron jumps from an orbit where n = 1 to n = 4, its energy in terms of the energy of the ground level E1 is
a. $E_{1/9\ }$
b. $2E_1$
c. $\mathbf{4E_1}$
d. $\mathbf{4E_1}$
9: How much of the universe is comprised of matter and energy that is explained by current Physics theory
a. 95 %
b. 75 %
c. 50 %
d. 5 %
10: The kinetic energy of photoelectrons depends on the
a. Speed of light
b. Intensity of the light
c. Number of incident photons
d. Photon frequency
11: The dynamical variables are real quantities that are measurable and so they are represented by
a. Hermitian operator
b. Anti-Hermitian operator
c. Linear operator
d. Non-linear operator
12: The maximum number of linearly independent vectors of a vector space is called − − − − − of vector space
a. Dimension
b. Basis
c. Modulus
d. None of these
13: A set of vectors in a vector space is called
a. Dimension
b. Basis
c. Modulus
d. Probability
14: Heisenberg uncertainty principle is a direct consequence of − − − − − of operators
a. Commutivity
b. Non commutivity
c. Probability
d. Conductivity
15: The eigen values of Apnti Hermitian operator are always
a. Complex
b. Real
c. Imaginary
d. All of above
16: The eigen values of Hermitian operator are always
a. Complex
b. Real
c. Imaginary
d. All of above
17: The eigen values of operators corresponding to dynamical variables are
a. Complex
b. Real
c. Imaginary
d. All of above
18: The bra space is − − − − − − − to kept space
a. Hilbert space
b. Vector space
c. Dual space
d. All of above
19: Which one of the following is not a Hermitian operator
a. Position
b. Momentum
c. Projection
d. Unitary
20: If two vectors are normalized and orthogonal, we called them − − − − − − − vectors
a. Normalized
b. Orthogonal
c. Orthonormal
d. None of these
21: If two operators are commute with each other, they possess a −−−−−−− eigenstate
a. Degenerate
b. Non-degenerate
c. Simultaneous
d. Orthogonal
22: Equation $\hat{A}\psi=\lambda\psi$ is called −−−−−−− equation
a. Expectation value
b. Operator
c. Wave function
d. Eigen value
23: Expectation value of an observable is always
a. Imaginary
b. Complex
c. Real
d. Commutative
24: In Schrodinger Picture, the wavefunctions are time dependent while − − − − − − − are time independent
a. Operators
b. Wave functions
c. Eigen values
d. None
25: In Heisenberg Picture, the operators are time dependent while −−−−−−− are time independent
a. Wave functions
b. Operators
c. Eigen values
d. None
26: In Interaction Picture, both − − − − − − − are time dependent
a. Eigen values, Wave functions
b. Operators, Wave functions
c. Eigen values, Operators
d. None
27: The solution of time dependent Schrodinger equation for a time independent potential is − − − − − − − state
a. Bound
b. Unbound
c. Stationary
d. All of above
28: The states corresponding to discrete spectra are called − − − − − − − states
a. Bound
b. Unbound
c. Stationary
d. All of above
29: The states corresponding to Continuous spectra are called − − − − − − − states
a. Bound
b. Unbound
c. Stationary
d. All of above
30: If transformation from one orthonormal set into another is unitary, such transformation is
a. Linear
b. Non linear
c. Unitary
d. Similarity
31: In one dimensional problem the energy levels of a bound state system are discrete and
a. Degenerate
b. Non degenerate
c. Complete
d. None
32: In one dimensional problem the energy levels of unbound state system are continuous and
a. Degenerate
b. Non degenerate
c. Complete
d. None
33: Unbound states occur in those cases where the motion of system is not confined example is
a. Step potential
b. Potential barrier
c. Free Particle
d. All of above
34: In one dimensional problem the energy levels of unbound state system (V1 < E < V2) are continuous and
a. Degenerate
b. Non degenerate
c. Complete
d. None
35: Bound states occur in those cases where the motion of system is confined; example is
a. Particle in a box
b. Infinite Square Well
c. Free Particle
d. Both a and b
36: When V (x) is even, the corresponding Hamiltonian is
a. Odd
b. Even
c. Degenerate
d. Non degenerate
37: The Number operator N is − − − − − − − operator
a. Parity
b. Projection
c. Identity
d. Hermitian
38: The sum of Reflection (R) and Transmission (T) Coefficients is equal to
a. 0
b. 1
c. Both a and b
d. None
39: The action of a on |n > generates a new state |n-1 > with value
a. n
b. n-1
c. $\mathbf{\sqrt n}$
d. $\sqrt{n-1}$
40: The action of a on |n> generates a new state |n + 1> with value
a. n
b. n+1
c. $\sqrt n$
d. $\sqrt{n+1}$
41: The Position and Momentum operators are always
a. Commutative
b. Anti Commutative
c. Normalized
d. Orthogonal
42: Expression for z-component of angular momentum is
a. $\mathbf{-i\hbar\frac{\partial}{\partial\phi}}$
b. $-i\hbar\frac{\partial}{\partial\theta}$
c. $i\hbar\frac{\partial}{\partial\phi}$
d. $i\hbar\frac{\partial}{\partial\theta}$
43: Components of angular momentum are
a. Orthogonal
b. Normal
c. Commute
d. Anti Commute
44: Value of L X L is
a. 0
b. 1
c. $i\hbar L$
d. All of above
45: The angular momentum of an isolated system is
a. Conserved
b. Non-Conserved
c. Variable
d. None
46: Spin does not depend on
a. S
b. $m_s$
c. spatial degrees of freedom
d. All of above
47: For Hydrogen atom that are in ground state, the orbital angular momentum will be
a. 1
b. 2
c. 0
d. Unknown
48: If azimuthal quantum number (l) is 2, the number of values of the magnetic quantum number will be
a. 2
b. 3
c. 4
d. 5
49: Square of angular momentum is
a. Hermitian
b. Anti Hermitian
c. Linear
d. Projection Operator
50: The square of angular momentum (J2) commutes with
a. $J_x$
b. $J_y$
c. $J_z$
d. All of these
51: Application of Barrier Tunneling are
a. Radioactive Decay
b. Semiconductor Devices
c. Both a and b
d. none
52: The energy of free particle in 3D is
a. Triply degenerate
b. Non degenerate
c. Infinitely Degenerate
d. None
53: The Centrifugal potential depends on − − −− quantum number
a. Orbital
b. Magnetic
c. Principle
d. All of above
54: Three dimensional problems often exhibit degeneracy, which occur whenever − − −− is symmetric
a. Eigen value
b. Wavefunction
c. Potential
d. None
55: Value of square of any Pauli spin matrix is − − −− matrix
a. Null
b. Diagonal
c. Identity
d. None
56: As the particle angular momentum increases, the particle becomes less and less
a. Repulsive
b. unbound
c. bound
d. Both a and b
57: Eigen values of square of spin angular momentum are
a. $\mathbf{s\left(s+1\right)2\hbar^2}$
b. $s\left(2s+1\right)\hbar^2$
c. $s\left(s+1\right)\hbar^2$
d. $s\left(2s+1\right)\hbar^2$
58: Radial equation for central potential depends on − − − − − − − quantum number
a. Azimuthal
b. Magnetic
c. Spin
d. None
59: The Hamiltonian of rigid rotator
a. $\hat{H}=\frac{{\hat{L}}^2}{4I}$
b. $\hat{H}=\frac{\hat{L}}{4I}$
c. $\mathbf{\hat{H}=\frac{{\hat{L}}^2}{2I}}$
d. $\hat{H}=\frac{\hat{L}}{8I}$
60: The quantized energy of rigid rotator is
a. $\mathbf{\frac{\hbar^2\left(l+1\right)}{2I}}$
b. $\frac{\hbar l\left(l+1\right)}{2I}$
c. $\frac{\hbar^2l\left(l+1\right)}{4l}$
d. $\frac{\hbar^2l\left(l+1\right)}{6I}$
61: The principle that all microscopic physical entities have both wave and particle properties is called the wave-particle:
a. Singularity
b. duality
c. Triality
d. Infinality
62: The full Schrodinger’s equation in compact form is:
a. $H\Psi=i\hbar\frac{\partial\Psi}{\partial t}$
b. $H\Psi=\hbar\frac{\partial\Psi}{\partial t}$
c. $H\Psi=i\frac{\partial\Psi}{\partial t}$
d. $H\Psi=-i\hbar\frac{\partial\Psi}{\partial t}$
63: In the probabilistic interpretation of wave function \Psi the quantity \left|\Psi\right|^2 is:
a. Probability density
b. Probability amplitude
c. Negative probability
d. 1
64: The probability of finding a particle in differential region dx is :
a. $\Psi\left(x,t\right)$dx
b. $\Psi\left(x,t\right)^\ast$ dx
c. $\frac{\Psi\left(x,t\right)^\ast}{\Psi(x,t)}$dx
d. $\mathbf{\Psi}\left(\mathbf{x},\mathbf{t}\right)^\ast\mathbf{\Psi}\left(\mathbf{x},\mathbf{t}\right)\mathbit{dx}$
65: A physical requirement on wave functions is that they should be:
a. Reliable
b. Square Integrable
c. Zero
d. Discrete
66: The charge on an electron is represented by e which of the following charges can exist:
a. 2.0 e
b. 2.5\ e
c. 3.6\ e
d. 5.2\ e
67: The energy of phonons depend upon its
a. Amplitude
b. Speed
c. Temperature
d. Pressure
68: When an electron jumps from an orbit where n=1 to n=4 its energy in terms of the energy of ground level E1 is:
a. $\frac{E1}{9}$
b. 2E1
c. 4E1
d. 16E1
69: How much of the universe is comprised of matter and energy that is explained by current physics theory:
a. 95%
b. 75%
c. 50%
d. 5%
70: The Kinetic energy of photo-electrons depend on the:
a. Speed of light
b. intensity of light
c. number of incident photon
d. photon frequency
71: The dynamical variables are real quantities that are measurable and so they are represented by:
a. Hermitian operator
b. Anti-Hermitian Operator
c. Linear operator
d. Non-linear Operaor
72: The maximum number of linearly independent vectors of a vector space is called……….. of vector space:
a. Dimension
b. basis
c. modulus
d. none of these
73: A set of vectors in a vector space is called:
a. Dimension
b. basis
c. modulus
d. probability
74: Heisenberg uncertainity principle is a direct consequence of ………….. of operators:
a. Commutivity
b. Non-commutivity
c. Probability
d. Conductivity
75: The eigen values of anti-hermitian operator are always:
a. Complex
b. Real
c. Imaginary
d. All of these
76: The eigen values of hermitian operator are always:
a. Complex
b. Real
c. Imaginary
d. All of these
77: The eigen values of operators corresponding to dynamical variables are:
a. Complex
b. Real
c. Imaginary
d. All of these
78: The bra space is ………………….. to ket space:
a. Hilbert space
b. Vector space
c. Dual space
d. All of these
79: Which one of the following is not a hermitian operator:
a. Position
b. Momentum
c. Projection
d. Unitary
80: If two vectors are normalized and orthogonal we called them ……….. vectors:
a. Normalized
b. Orthogonal
c. Orthonormal
d. None of these
81: If two operators commute with each other they possess a…………. eigen state:
a. Degenerate
b. Non-degenerate
c. Simultaneous
d. Orthogonal
82: In equation $\hat{A}\Psi=\lambda$ Psi is called:
a. Expectation value
b. Operator
c. Wave function
d. Eigen value
83: Expectation value of an observable is always:
a. Imaginary
b. Complex
c. Real
d. Commutative
84: In schrodinger picture the wavefunctions are time dependent while ………. Are time independent:
a. Operators
b. Wavefunctions
c. Eigen values
d. None
85: In Heisenberg picture the operators are time dependent while……… are time independent:
a. Wavefunctions
b. Operators
c. Eigen values
d. None
86: In interaction picture both …………….. are time dependent:
a. Eigen values, wavefunctions
b. Operators, wavefunctions
c. Eigen values, operators
d. None
87: The solution of time dependent Schrodinger equation for a time independent solution is …..… state:
a. Bound
b. Unbound
c. Stationary
d. All of these
88: The states corresponding to discrete spectra are called …………….. states:
a. Bound
b. Unbound
c. Stationary
d. All of these
89: The states corresponding to continuous spectra are called …………… states:
a. Bound
b. Unbound
c. Stationary
d. All of these
90: If transformation from one orthonormal set into another is unitary such transformation is:
a. Linear
b. Non-linear
c. Unitary
d. Similarity
91: In one dimensional problem the energy levels of a bound state system are discrete and:
a. Degenerate
b. Non-degenerate
c. Complete
d. None
92: In one dimensional problems the energy levels of bound state system \left(E>V\right) are continuous and:
a. Degenerate
b. Non-degenerate
c. Complete
d. None
93: Unbound states occur in those cases where the motion of system is not confined; example is:
a. Step potential
b. Potential barrier
c. Free particle
d. All of these
94: In one dimensional problem the energy levels of unbound state system \left(V_1<E<V_2\right) are continuous and:
a. Degenerate
b. Non-degenerate
c. Complete
d. None
95: Bound states occur in those cases where the motion of a system is confined; example is:
a. Particle in a box
b. Infinite square well
c. Free particle
d. Both a & b
96: When $V\left(x\right)$ is even the corresponding Hamiltonian is:
a. Odd
b. Even
c. Degenerate
d. Non-degenerate
97: The number operator N is ……………. Operator:
a. Parity
b. Projection
c. Identity
d. Hermitian
98: The sum of reflection and transmission![]()
coefficients is equal to:
a. 0
b. 1
c. Both a and b
d. None
99: The action a on |n> generates a new state |n-1> with value:
a. n
b. n-1
c. $\sqrt\mathbit{n}$
d. $\sqrt{n-1}$
100: The action a on |n> generates a new state |n+1> with value:
a. n
b. $\sqrt n$
c. $\sqrt{\mathbit{n}+\mathbf{1}$
d. n+1
101: The position and momentum operator are always :
a. Commutative
b. Anti-commutative
c. Normalized
d. Orthogonal
102: Expression for $-\mathbit{i}\hbar\frac{\partial}{\partial\phi}$ of angular momentum is:
a. $-i\hbar\frac{\partial}{\phi\theta}$
b. $i\hbar\frac{\partial}{\partial\phi}$
c. $i\hbar\frac{\partial}{\phi\theta}$
d. $i\hbar\frac{\partial}{\phi\theta}$
103: Components of angular momentum are:
a. Orthogonal
b. Normal
c. Commute
d. Anti-commute
104: Value of $L\times L$ is:
a. 0
b. 1
c. $i\hbar L$
d. All of these
105: The angular momentum of an isolated system is:
a. Conserved
b. Non-conserved
c. Variable
d. None
106: Spin does not depend on:
a.$J_x$
b. $J_y$
c. Spatial degrees of freedom
d. All of these
107: For hydrogen atom that are in ground state the orbital angular momentum will be:
a. 1
b. 2
c. 0
d. Unknown
108: If azimuthal quantum number is 2 the number of values of magnetic quantum number will be:
a. 2
b. 3
c. 4
d. 5
109: Square of angular momentum is:
a. Hermitian
b. Anti-Hermitian
c. Linear
d. Projection Operator
110: The application of barrier tunneling are:
a. Radioactive decay
b. Semiconductor devices
c. Both a & b
d. None
111: The energy of free particle in 3D is:
a. Triply degenerate
b. Non-degenerate
c. Infinitely degenerate
d. None
112: The centrifugal potential depends on…….. quantum number:
a. Orbital
b. Magnetic
c. Principle
d. All of these
113: Three dimensional problems often exhibit degeneracy which occur whenever …….is symmetric:
a. Eigen values
b. Wavefunctions
c. Potential
d. None
114: Value of square of any Pauli spin matrix is……… matrix:
a. Null
b. Diagonal
c. Identity
d. None
115: As the particle angular momentum increases the particles becomes less and less:
a. Repulsive
b. Unbound
c. Bound
d. Both a and b
116: Eigen values of square of spin angular momentum are:
a. $\mathbf{S}(\mathbf{S}+\mathbf{1})\mathbf{2}\hbar^\mathbf{2}$
b. $S\left(2S+1\right)\hbar^2$
c. $S\left(S+1\right)\hbar^2$
d. $2S(S+1)\hbar^2$
117: Radial equation for central potential depends on……… quantum number:
a. Azimuthal
b. Magnetic
c. Spin
d. None
118: The Hamiltonian of rigid rotator:
a. $\hat{H}=\frac{{\hat{L}}^2}{4I}$
b. $\hat{H}=\frac{\hat{L}}{4I}$
c. $\hat{\mathbf{H}}=\frac{{\hat{\mathbf{L}}}^\mathbf{2}}{\mathbf{2I}}$
d. $\hat{H}=\frac{\hat{L}}{8I}$
119: The quantized energy of rigid rotator is:
a. $\frac{\hbar^\mathbf{2}\mathbit{l}\left(\mathbit{l}+\mathbf{1}\right)}{\mathbf{2}\mathbit{l}}$
b. $\frac{\hbar l\left(l+1\right)}{2l}$
c. $\frac{\hbar^2l\left(l+1\right)}{4l}$
d. $\frac{\hbar^2l\left(l+1\right)}{6l}$
120: A photocell is illuminated by a source 1m away. When a source is taken 2m away:
a. The number of electrons emitted is quarter of the initial number
Hint: $\left(\mathbf{As}\ \ \mathbit{I}\propto\frac{\mathbf{1}}{\mathbit{r}^\mathbf{2}}\right)$
a. The number of electrons is emitted is a half of initial number
b. Each electron emitted carries one quarter of the initial energy
c. Each electron emitted carries double of the initial energy
121: Photoelectric effect supports quantum nature of light because:
a. There is minimum of light below which no photoelectrons are emitted
b. Electric charge of photoelectrons is quantized
c. Maximum kinetic energy of photoelectrons depends only on frequency of light and not on its intensity
d. a and c
122: The process of photoelectric emission depends upon:
a. Wavelength of incident light
b. Work function of surface
c. Nature of surface
d. All of above
123: Which of the following achieve conversion of electromagnetic wave energy into electrical energy:
a. Photocell
b. Coolidge tube
c. C.R.O
d. Vacuum tube
124: The wavelength of matter waves does not depend on:
a. Mass
b. Charge
c. Momentum
d. Velocity
125: If value of plank’s constant is more than present value the De-Broglie wavelength associated with a material particle will be:
a. Less
b. More
c. Same
d. None of these
126: The De-Broglie wavelength of an electron is 0.2Ao. The de-celerating potential to stop it will be:
a. -3762V
b. -1000V
c. -4000V
d. -2000V
127: Which of the following will have the shortest wavelength while moving with the same speed:
a. Proton
b. Neutron
c. Deuteron
d. Electron
128: The waves associated with moving particles are known as:
a. Sound waves
b. Matter waves
c. Electromagnetic waves
d. Stationary waves
129: The wave nature of electrons was verified by:
a. Electron diffraction experiments
b. Compton effect
c. Photoelectric effect
d. None of these
130: The ratio of velocities of a proton and alpha particle is 4:1. The ratio of their De-Broglie wavelength will be:
a. 1:2
b. 1:4
c. 1:1
d. 4:1
132: The De-Broglie wavelength of a neutron at 27 degc . Its wavelength at 927\degc will be:
a. $\frac{\lambda}{9}$
b. $\frac{\lambda}{4}$
c. $\frac{\lambda}{3}$
d. $\frac{\mathbit{\lambda}}{\mathbf{2}}$
Hint: $\left(\mathbf{\lambda}=\frac{\mathbf{h}}{\sqrt{\mathbf{2m}\ \mathbf{k}_\mathbf{B}\mathbf{T}}}\right)$
133: The hypothesis regarding dual nature of material was proposed by:
a. De-Broglie
b. Davisson
c. Germer
d. Heisenberg
134: The waves associated with electrons revolving in various Bohr’s orbits in an atom are:
a. Stationary
b. Transverse
c. Longitudinal
d. Progressive
135: Which of the following properties of electron is made use of electron microscope:
a. High velocity
b. Wave nature
c. Diffraction
d. Interference
135: The wavelength of a photon, electron and uranium nucleus are equal. The minimum energy is associated with:
a. Electron
b. Photon
c. Uranium
d. All of these
136: An electron in hydrogen atom makes a transition from an excited state to ground state. Which of the following statement is true:
a. Its kinetic energy decreases, potential energy increases and total energy remains same
b. Its kinetic energy increases, potential energy and total energy decreases
c. Its kinetic energy and total energy decreases, potential energy increases
d. Its kinetic, potential and total energies decrease
137: Three photons coming from excited atomic hydrogen sample are picked up their energies are 12.1eV, 10.9eV and 1.9eV. These photons must come from:
a. Single atom
b. Two atoms
c. Three atoms
d. Either two or three atoms
138: The quantity $\left|\Psi(x,t)\right|^2$ is called:
a. Probability density
b. Probability current density
c. Probability
d. All of these
139: The quantity $\left|\Psi(x,t)\right|^2$dx is called:
a. Probability density
b. Probability current density
c. Probability
d. All of these
140: The condition $\int_{-\infty}^{+\infty}{\Psi^\ast(x,t)\Psi(x,t)dx}=1$ is called:
a. Normalization condition
b. Probability density condition
c. Probability
d. All of these
141: The Schrodinger wave equation is:
a. $\hat{H}\Psi=E\Psi$
b. $-\frac{\hbar^2}{2m}\nabla^2\Psi+V\Psi=E\Psi$
c. $-\frac{\hbar^2}{2m}\nabla^2\Psi+V\Psi=i\hbar\frac{\partial\Psi}{\partial t}$
d. all of these
142: The dynamical variables are real quantities that are measurable and so they are represented by:
a. Hermitian operators
b. Anti-hermitian operators
c. Non-linear operators
d. None
143: A measurement of identical states need not give identical results but only identical:
a. Probability distributions
b. Charge distributions
c. Momentum distributions
d. Velocity distributions
144: Position and momentum of an electron cannot be measured simultaneously. This is statement of:
a. Uncertainty principle
b. Ehrenfest theorem
c. Bohr postulate
d. None
145: Heisenberg uncertainty principle is a direct consequence of ………….. of operators corresponding to canonically conjugate variables:
a. Commutivity
b. Non-commutivity
c. Conductivity
d. None of these
146: Heisenberg has proposed certain though experiments known as………… to illustrate the principle of uncertainty:
a. Gedanken experiments
b. Bohr experiments
c. Deuteron experiments
d. Electron experiments
147: A given state of a physical system is represented by a vector in multi-dimensional complex linear vector space with an orthonormal basis called:
a. Vector space
b. Euclidean space
c. Inner product space
d. Hilbert space
148: The result of measurement of an observable quantum mechanical system in a particular state is given by…………. Value of corresponding Hermitian operator in that state:
a. Eigen
b. Expectation
c. Characteristic
d. None of these
149: The time evaluation of state vector \Psi of a system is governed by equation:
a. $-\mathbf{i}\hbar\frac{\partial\Psi\left(\mathbf{t}\right)}{\partial t}=\hat{\mathbf{H}}\mathbf{\Psi}(\mathbf{t})$
b. p=mv
c. $\lambda=\frac{h}{mv}$
d. All of these
150: In equation $\hat{A}\Psi=\lambda\Psi$, $\lambda$ is called:
a. Expectation value
b. Eigen value
c. a & b
d. None of these
150: The Eigen values of operators corresponding to dynamical variables are:
a. Complex
b. Integers
c. Real
d. All of these
151: Any arbitrary wave function of physical interest can always be written as……….. of eigen vectors of operators corresponding to dynamical variables of a system:
a. Linear combination
b. Superposition
c. a & b
d. None of these
152: The Eigen values of Hermitian operator are always:
a. Complex
b. Integers
c. Real
d. All of these
153: It is necessary for two operators to commute with each other for having a………..
a. Degenerate Eigen value
b. Simultaneous Eigen functions
c. Orthogonal Eigen functions
d. All of these
154: The quantum theory will give the results identical to classical theory if masses and dimensions of system under consideration are made to approach the ………….. size:
a. Microscopic
b. Macroscopic
c. a & b
d. None of these
155: Corresponding to every observable there exists a Hermitian operator. The only measurable values of a physical observable are the various………… values of corresponding operator:
a. Expectation
b. Eigen
c. a & b
d. None of these
156: For a system consisting of a particle moving in a field of conservative force there is an associated complex wave function $\Psi(x,y,z,t)$ where x,y,z are space coordinates and “t” is time. This function enables us to obtain a description of the behavior of the system consistent with:
a. Uncertainty principle
b. Ehrenfest theorem
c. Bohr postulate
d. None of these
157: Let V1 & V2 be two distinct vector spaces. The vector space obtained by multiplying element of V1by every element of V2 is called………… of V1 with V2:
a. Density product
b. Direct product
c. Probability
d. All of these
158: The number of basis vectors of a vector space is called……….. of vector space:
a. Dimensionality
b. Current density
c. Probability
d. None of these
159: The positive square root of scalar product of a vector with itself is called………… of vector:
a. Normalization condition
b. Probability condition
c. Norm
d. Modulus
160: If two vectors are normalized and orthogonal also we call them…….. vectors:
a. Normalized
b. Orthogonal
c. Orthonormal
d. None
161: The Bra space is ………… to Ket space:
a. Hilbert space
b. Vector space
c. Dual space
d. None
162: If determinant of a matrix is zero it is called:
a. Non-singular matrix
b. Singular matrix
c. Eigen value
d. Velocity distribution
163: The matrix transforming one orthonormal set into another is unitary and the transformation of this type is termed as:
a. Unitary transformation
b. Similarity transformation
c. Bohr postulate
d. None
164: In Schrodinger picture the…………. Are time dependent while ……… are time independent:
a. Wave function, Operator
b. Operator, Wave function
c. a & b
d. None
165: In Heisenberg picture the……….. are time dependent while………. Are time independent:
a. Wave function, Operator
b. Operator, Wave function
c. a & b
d. None
166: The operator $\hat{a}=\frac{1}{\sqrt{2\hbar m\omega}}(m\omega x+ip)$ is called:
a. Raising operator
b. Lowering operator
c. Inner product operator
d. Hilbert operator
167: A free particle cannot exist in a stationary state or to put it another way there is no such thing as a free particle with a definite:
a. Energy
b. Momentum
c. Acceleration
d. All of these
168: Generating function for Hermite polynomials is:
a. $e^{-t^2+2xt}=\sum_{n=0}^{\infty}\frac{t^n}{n!}H_n(x)$
b. $e^{-t^2-2xt}=\sum_{n=0}^{\infty}\frac{t^n}{n!}H_n(x)$
c. $e^{-t^2+2xt}=\sum_{n=0}^{\infty}\frac{t^n}{n!}H_n\left(ax\right)$
d. None of these
169: In one dimensional problem the energy levels of a bound state system are discrete and………..:
a. Degenerate
b. Non-degenerate
c. Orthogonal
d. Complete
170: Unbound states occur in those cases where the motion of a system is not confined, a typical example is:
a. Step potential
b. Potential barrier
c. Free particle
d. All of these
171: The ladder operator $\hat{a}=\frac{1}{\sqrt2}\left(\hat{q}-i\hat{p}\right)$ is called:
a. Raising operator
b. Lowering operator
c. a & b
d. None of these
172: The number operator $\hat{N}={\hat{a}}^\dag\hat{a}$ is……….. operator:
a. Unitary
b. Projection
c. Hermitian
d. All of these
173: A wave function \psi(x) is acceptable if it is:
a. Integrable
b. Single valued and continuous
c. Differentiable
d. All of these
174: For a particle subject to delta potential $V\left(x\right)=-V_o\delta\left(x\right), V_o>0$, for non-negative energies the particle has:
a. Two unbound states
b. Only one bound state
c. a & b
d. None of these
174: Applications of barrier tunneling are:
a. Radioactive decays
b. Semiconductor devices
c. a & b
d. None of these
175: In case of harmonic oscillator the conditions $\psi\left(x_{min}\right)=0, \psi\left(x_{min}\right)=0$, are satisfied as follows:
a. $\mathbf{\psi}\left(-\infty\right)=\mathbf{0}=\mathbf{\psi}\left(+\infty\right)$
b. $\psi\left(-a\right)=0=\psi\left(+a\right)$
c. $\psi\left(-\frac{a}{2}\right)=0=\psi\left(+\frac{a}{2}\right)$
d. None of these
176: The operator for angular momentum is:
a. $-i\hbar r\hat{r}\times\nabla$
b. $-i\hbar r\times\nabla$
c. -$\frac{\hbar}{i}r\hat{r}\times\nabla$
d. All of these
177: Components of angular momentum are:
a. Orthogonal
b. Anti-commute
c. Do not commute
d. None of these
178: Value of $\hat{L}\times\hat{L}$ is:
a. Zero
b. One
c. $-\mathbf{i}\hbar\hat{\mathbf{L}}$
d. None of these
179: Square of angular momentum is:
a. Hermitian
b. Projection operator
c. Unitary operator
d. All of these
180: Expression of z-component of angular momentum is:
a. $-\mathbf{i}\hbar\frac{\partial}{\partial\varphi}$
b. $-i\hbar\frac{\partial}{\partial\theta}$
c. $-i\hbar\frac{\partial}{\partial z}$
d. None of these
