Quantum Mechanics-Time-Independent Perturbation Theory (GATE Physics): Questions 1 - 3 of 5

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Question number: 1

» Quantum Mechanics » Time-Independent Perturbation Theory

Appeared in Year: 2014

MCQ▾

Question

A particle is confined to a one dimensional potential box with the potential

V(x)={0,0<x<a,otherwise

If the particle is subjected to a perturbation, within the box, W=βx , where β is a small constant, the first order correction to the ground state energy is –

Choices

Choice (4) Response
a.

0

b.

αβ2

c.

αβ4

d.

αβ

Question number: 2

» Quantum Mechanics » Time-Independent Perturbation Theory

Appeared in Year: 2012

MCQ▾

Question

Consider a system in the unperturbed state described by the Hamiltonian, H0=(1001) . The system is subjected to a perturbation of the form H=(δδδδ) where δ1 . The energy eigenvalues of the perturbed system using the first order perturbation approximation are –

Choices

Choice (4) Response
a.

(1+δ)and(1δ)

b.

(1+δ)and(12δ)

c.

1and(1+2δ)

d.

(1+2δ)and(12δ)

Question number: 3

» Quantum Mechanics » Time-Independent Perturbation Theory

Appeared in Year: 2011

MCQ▾

Question

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

V(x)={0;if0xa;otherwise

are given by, ψn(x)=2asin(nπxa) , where n=1, 2,3

The particle is subjected to a perturbation,

V(x)={V0cos(πxa);for0xa20;otherwise

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

Choices

Choice (4) Response
a.

2V03π

b.

2V03π

c.

V03π

d.

V03π

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