Quantum Mechanics MCQs with Answers 2027

Q21

For a perfect free electron gas in a metal the magnitudes of phase velocity (v_p) and group velocity (v_g) are such that

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Q22

Open question

The time independent Schrodinger equation of a system represents the conservation of the

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Q23

Open question

Which of the following functions represents acceptable wave function of a particle in the range

- \infty ⩽ x ⩽ \infty ?

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Q24

Open question

The wave function of a particle moving in a one-dimensional time independent potential V(x) is given by

ψ (x) = e^{- ia x + b},

where a and b are constants. This means that the potential V(x) is of the form

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Q25

Open question

The commutator [x, p²], where x and p are position and momentum operators respectively, is

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Q26

Open question

The de-Broglie wavelength of particles of mass m with average momentum p at a temperature T in three-dimensions is given by

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Q27

Open question

The Hamiltonian of a particle is given by

H = \frac{p ^{2}}{2 m} + V (r) + ϕ (+ r) L . S,

where

S

is the spin,

V (r)

and

ϕ (r)

are potential functions and

L (= r \times p)

is the angular momentum. The Hamiltonian does not commute with

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Q28

Open question

Which of the following is an allowed wave function for a particle in a bound state? N is a constant and α, β > 0.

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Q29

Open question

The de-Broglie wavelength λ for an electron of energy 150 eV is

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Q30

Open question

The radial wave function of the electrons in the state of n = 1 and 1 = 0 in hydrogen atom is

R_{10} = \frac{2}{a _{0}^{\frac{3}{2}}} exp (- \frac{r}{a _{0}}), a_{0}

is the Bohr radius. The most probable value of r for an electron is

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Q31

Open question

A^

and

B^

are two quantum mechanical operators. If

[A^, B^]

stands for the commutator of

A^

and

B^

then

[[A^, B^], [B^, A^]]

is equal to

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Q32

Open question

The parities of the wave functions (i) cos (kx) and (ii) tanh (kx) are

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Q33

Open question

The commutator

[L_{z}, Y_{l m} (θ, ϕ)],

where L_z is the z component of the orbital angular momentum and

Y_{l m} (θ, ϕ)

is a spherical harmonic, is

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Q34

Open question

A particle is in the normalized state

∣ ψ ⟩

which is a superposition of the energy eigen states

∣ E_{0} = 10 e V ⟩

and

∣ E_{1} = 30 e V ⟩ .

The average value of energy of the particle in the state

∣ ψ ⟩

is 20 eV. The state

∣ ψ ⟩

is given by

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Q35

Open question

If L_x, L_y and L_z are respectively the x, y and z components of angular momentum operator L, the commutator [L_x, L_y, L_z] is equal to

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Q36

Open question

The wave function of a particle in a one-dimensional potential at time t = 0 is

ψ (x, t = 0) = \frac{1}{15} [2 ψ_{0} (x) - ψ_{1} (x)]

where,

ψ_{0} (x)

and

ψ_{1} (x)

are the ground arid the first excited states of the particle with corresponding energies E₀ and E₁. The wave function of the particle at a time t is

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Q37

Open question

An electron in a time independent potential is in a state which is the superposition of the ground state (E₀ = 11 eV) and the first excited state (E₁ = 1 eV). The wave function of the electron will repeat itself with a period of

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Q38

Open question

Consider the combined system of proton and electron in the hydrogen atom in its (electronic) ground state. Let

I

denotes the quantum number associated with the total angular momentum and let

< M >

denote the magnitude of the expectation value of the net magnetic moment in the state. Which of the following pairs represents a possible state of the system (

μ_{B}

is Bohr magneton)?

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Q39

Open question

If [x, p] =

i ℏ,

the value of [x³, p] is

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Q40

Open question

Three operators X, Y and Z satisfy the commutation relations,

[X, Y] = i ℏ Z, [Y, Z] = i ℏ X

and

[Z, X] = i ℏ Y .

The set of all possible eigen values of the operator Z, in units of

ℏ

is

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Quantum Mechanicspractice.

Quantum Mechanics
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