Quantum Mechanics [GATE (Graduate Aptitude Test in Engineering) Physics]: Questions 26 - 31 of 80

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Question 26

Appeared in Year: 2011

Question

MCQ▾

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

are given by, , where

The particle is subjected to a perturbation,

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

Choices

Choice (4)Response

a.

b.

c.

d.

Passage

To the given unperturbed Hamiltonian , we add a small perturbation given by, ; where is a small quantity.

Question 27 (1 of 2 Based on Passage)

Appeared in Year: 2013

Question

MCQ▾

A pair of eigenvalues of the perturbed Hamiltonian, using first order perturbation theory, is –

Choices

Choice (4)Response

a.

b.

c.

d.

Question 28 (2 of 2 Based on Passage)

Appeared in Year: 2013

Question

MCQ▾

The ground state eigenvector of the unperturbed Hamiltonian is –

Choices

Choice (4)Response

a.

b.

c.

d.

Question 29

Appeared in Year: 2013

Question

MCQ▾

Which one of the following commutation relation is NOT CORRECT? Here, symbols have their usual meanings.

Choices

Choice (4)Response

a.

b.

c.

d.

Question 30

Quantum Mechanics

Appeared in Year: 2013

Write in Short

Short Answer▾

Consider the wave function , where is the normalization constant. For , the magnitude of probability current density up to two decimal places, in unit of , is ________.

Question 31

Appeared in Year: 2013

Write in Short

Short Answer▾

A spin – half particle is in a linear superposition of its spin – up and spin – down states. If and are the eigenstate of then what is the expectation value, up to one decimal place, of the operator ? Here, symbols have their usual meaning.

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