Quantum Mechanics-Particle in a Box (GATE Physics): Questions 1 - 3 of 5

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Question number: 1

» Quantum Mechanics » Particle in a Box

Appeared in Year: 2015

MCQ▾

Question

A particle is confined in a box of length L as shown below,

A particle is in box

A Particle Is in Box

In figure a particle is confined in a box pf length L is shown.

If the potential V0 is treated as a perturbation, including the first order correction, the ground state energy is –

Choices

Choice (4) Response

a.

E=2π22mL2+V02

b.

E=2π22mL2V02

c.

E=2π22mL2+V0

d.

E=2π22mL2+V04

Question number: 2

» Quantum Mechanics » Particle in a Box

Appeared in Year: 2010

MCQ▾

Question

A particle of mass m is confined in the potential V(x)={12mω2x2,forx>0,forx0 ,

Let the wavefunction of the particle be given by ψ(x)=15ψ0+25ψ1 , where ψ0 and ψ1 are the eigenfunctions of the ground state and the first excited state respectively. The expectation value of the energy is –

 Potential v/s position graph

Potential v/s Position Graph

In figure Graph of potential verses position is shown.

Choices

Choice (4) Response

a.

1110ω

b.

1310ω

c.

3110ω

d.

2510ω

Question number: 3

» Quantum Mechanics » Particle in a Box

Appeared in Year: 2010

MCQ▾

Question

A particle of mass m is confined in an infinite potential well V(x)={0,if0<x<L,otherwise , it is subjected to a perturbing potential VP(x)=V0sin(2πxL) within the well. Let E(1) and E(2) be the corrections to the ground state energy in the first and second order in V0 ,

Potential of particle in infinite potential well

Potential of Particle in Infinite Potential Well

In figure a potential of particle in infinite potential well is shown.

Choices

Choice (4) Response

a.

E(1)>0;E(2)=0

b.

E(1)=0;E(2)<0

c.

E(1)<0;E(2)<0

d.

E(1)=0;E(2) depends on the sign of V0

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