GATE PH topic:quantum-mechanics PYQs & Answers — Page 5

Home
GATE
Physics
Topics
topic:quantum-mechanics

Questions 41–50 of 83. Imported answers require independent review unless marked reviewed.

Topic practice 83 questionsPage 5 of 9

The wavefunction of a particle in a one-dimensional infinite well of size

at a certain time is

. Probability of finding the particle in

state at that time is ______% (Round off to the nearest integer)

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A student sets up Young’s double slit experiment with electrons of momentum

incident normally on the slits of width

separated by distance

. In order to observe interference fringes on a screen at a distance

from the slits, which of the following conditions should be satisfied?

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Consider a particle in three different boxes of width

. The potential inside the boxes are as shown in figures (i), (ii) and (iii) with

. The corresponding ground-state energies of the particle are

and

, respectively. Then

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

For a one-dimensional harmonic oscillator, the creation operator (

) acting on the

state

, where

, gives

. The matrix representation of the position operator

for the first three rows and columns is

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A particle of mass

is moving inside a hollow spherical shell of radius

so that the potential is

The ground state energy and wavefunction of the particle are

and

, respectively. Then which of the following options are correct?

Your answerSelect all correct options. You can choose more than one.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A particle of mass

in the

plane is confined in an infinite two-dimensional well with vertices at

. The eigenfunctions of this particle are

. If perturbation of the form

, where

is a real constant, is applied, then which of the following statements are correct for the first excited state?

Your answerSelect all correct options. You can choose more than one.

The unperturbed energy is

First order energy shift due to the applied perturbation is zero

The shift (

) in energy due to the applied perturbation is determined by an equation of the form

, where

and

are real, non-zero constants

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A matter wave is represented by the wave function

where

is a constant. The unit vector representing the direction of propagation of this matter wave is

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

is a solution of the differential equation

where

is an integer and the prime (

) denotes differentiation with respect to

, then acceptable plot(s) of

, is(are)

Your answerSelect all correct options. You can choose more than one.

Diagram for Physics question 16 (figure 2)

Diagram for Physics question 16 (figure 3)

Diagram for Physics question 16 (figure 4)

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Consider a spin

particle in the state

. The probability that a measurement finds the state with

Your answerChoose one option.

5/18

11/18

15/18

17/18

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Consider a particle in a one-dimensional infinite potential well with its walls at

and

. The system is perturbed as shown in the figure.

The first order correction to the energy eigenvalue is

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

GATE PH topic:quantum-mechanics PYQs

Question 34

Question 38

Question 39

Question 45

Question 48

Question 56

Question 2

Question 16

Question 28

Question 34