Quantum Mechanics MCQs with Answers 2027

Q1

A particle is placed in a one-dimensional box of size L along the X-axis, (0 < x < L). Which of the following is true?

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Q2

If the probability that x lies between x and x + dx is P(x) dx = ae^-ax dx, where 0 < x <

\infty

, a > 0, then the probability that x lies between x₁ and x₂ (x₂ > x₁) is

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Q3

Open question

A Michelson interferometer is illuminated with monochromatic light. When one of the mirrors is moved through a distance of 25.3 μm, 92 fringes pass through the cross-wire. The wavelength of the monochromatic light is

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Q4

Open question

An electron is in a statewith spin wavefunction

{\phi _s} = \left[ {\begin{array}{*{20}{c}} {\frac{{\sqrt 3 }}{2}} \\ {\frac{1}{2}} \end{array}} \right]

in the s_z representation. What is the probability of, finding the z-component of its spin along the

- Z^

direction?

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Q5

Open question

If the wave function of a particle trapped in space between x = 0 and x = L is given by

ψ (x) = A sin (\frac{2 π x}{L}),

where A is a constant, for which value(s) of x will the probability of finding the particle be the maximum?

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Q6

Open question

The normalized eigen states of a particle in a one-dimensional potential well

V\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {0,}&{{\text{if }}0 \leqslant x \leqslant a} \\ {\infty ,}&{{\text{otherwise}}} \end{array}} \right.

are given by

ψ_{n} (x) = \frac{2}{a} sin (\frac{nπ x}{a})

where, n = 1, 2, 3, . . .
The particle is subjected to a perturbation

V^{'} x = V_{0} cos (\frac{π x}{a}), for 0 ⩽ x ⩽ \frac{a}{2} = 0, otherwise

The shift in the ground state energy due to the perturbation, in the first order perturbation theory, is

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Q7

Open question

A parallel beam of electrons of a given momentum pass through a screen S₁ containing a slit and then produces a diffraction pattern on a screen S₂ placed behind it. The width of the central maximum observed on the screen S₂ can be increased by

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Q8

Open question

An exact measurement of the position of a Simple Harmonic Oscillator (SHO) is made with the result x = x₀, [The SHO has energy levels E_n (n = 0, 1, 2, . . .) and associated normalized wave functions

ψ_{n}

]. Subsequently, an exact measurement of energy E is made, using the general notation Pr(E = E') denoting the probability that a result E' is obtained for this measurement, the following statements are written. Which one of the following statements is correct?

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Q9

Open question

An atomic state of hydrogen is represented by following wave function

ψ (r, θ, ϕ) = \frac{1}{2} (\frac{1}{a _{0}})^{\frac{3}{2}} (1 - \frac{r}{2 a _{0}}) e^{\frac{- r}{2 a _{0}}} cos θ

where, a₀ is a constant. The quantum numbers of the state are

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Q10

Open question

A spinless particle moves in a central potential V(r).

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Q11

Open question

The expectation value of the z coordinate, (z), in the ground state of the hydrogen atom (wave function:

ψ_{100} (r) = A e^{- \frac{r}{a _{0}}},

where A is the normalization constant and

a_{0}

is the Bohr radius), is

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Q12

Open question

The resonance widths

Γ

of

ρ, ω

and

ϕ

particle resonances satisfy the relation

Γ_{ρ} > Γ_{ω} > Γ_{ϕ}

. Their lifetimes r satisfy the relation

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Q13

Open question

The spin' function of a free particle, in the basis in which s_z is diagonal can be written as

\left[ {\begin{array}{*{20}{c}} 1 \\ 0 \end{array}} \right]

and

\left[ {\begin{array}{*{20}{c}} 0 \\ 1 \end{array}} \right]

with eigen values

+ \frac{ℏ}{2}

and

- \frac{ℏ}{2}

respectively. In the given basis, the normalized eigen function of s_y with eigen value

- \frac{ℏ}{2}

is

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Q14

Open question

A one-dimensional harmonic oscillator is in the state

ψ (x) = \frac{1}{14} [3 ψ_{0} (x) - 2 ψ_{1} (x) + ψ_{2} (x)],

where,

ψ_{0} (x), ψ_{1} (x)

and

ψ_{2} (x)

are the ground, first excited and second excited states, respectively. The probability of finding the oscillator in the ground state is

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Q15

Open question

Which one of the following statements concerning the Compton effect is not correct?

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Q16

Open question

Let

L

= (L_x, L_y, L_z) denotes the orbital angular momentum operators of a particle and let L₊ = L_x + i L_y and L_- = L_x - i L_y. The particle is in aneigen state of L² and L_z eigen values

ℏ^{2} (l + 1)

and

ℏ l

respectively. The expectation value of L₊L_- in this state is

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Q17

Open question

A one-dimensional harmonic oscillator carrying a charge -q is placed in a uniform electric field

E

along the positive X-axis. The corresponding Hamiltonian operator is

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Q18

Open question

A spin half particle is in the state

S_{z} = \frac{ℏ ^{2}}{2} .

The expectation values of

S_{x}, S_{x}^{2}, S_{y}, S_{y}^{2}

are given by

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Q19

Open question

Let

∣ ψ_{0} ⟩

denotes the ground state of the hydrogen atom. Choose the correct statement from those given below.

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Q20

Open question

An electron propagating along the X-axis passes through a slit of width ∆y = 1 nm. The uncertainty in the y-component of its velocity after passing through the slit is

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Quantum Mechanicspractice.

Quantum Mechanics
practice.