Quantum Mechanics (CSIR Physical Sciences): Questions 47 - 50 of 70

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Question number: 47

» Quantum Mechanics » Timeindependent Perturbation Theory and Applications

Appeared in Year: 2013

MCQ▾

Question

A perturbation Vper=aL2 is added to the Hydrogen atom potential. The shift in the energy level of 2P state, when the effects of spin are neglected up to second order in a , is – (Dec. 2013)

Choices

Choice (4) Response
a.

a2+32a24

b.

2a2+a24

c.

2a2

d.

0

Question number: 48

» Quantum Mechanics » Eigenvalue Problems

Appeared in Year: 2013

MCQ▾

Question

If ψ(x)=Aexp(x4) is the eigenfunction of a one – dimensional Hamiltonian with eigenvalue E=0 , the potential V(x) (in units where =2m=1 ) is – (Dec – 2013)

Choices

Choice (4) Response
a.

16x612x2

b.

16x6+12x2

c.

12x2

d.

16x6

Question number: 49

» Quantum Mechanics » Eigenvalue Problems

Appeared in Year: 2013

MCQ▾

Question

A particle is prepared in a simultaneous eigenstate of L2 and Lz . If l(l+1) and m are respectively the eigenvalues of L2 and Lz , then the expectation value Lx2 of the particle in this state satisfies – (December -2013)

Choices

Choice (4) Response
a.

l22Lx2l(l+1)22

b.

Lx2=0

c.

0Lx2=l2

d.

0Lx2l(l+1)23

Question number: 50

» Quantum Mechanics » Timeindependent Perturbation Theory and Applications

Appeared in Year: 2013

MCQ▾

Question

Consider a two – dimensional infinite square well,

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

Its normalized eigenfunction are; ψnx,ny(x,y)=2asin(nxπxa)sin(nyπya)

Where, nx,ny=1, 2,3, If a perturbation H={V0,0<x<a2,0<y<a20,otherwise is applied, then the correction to the energy of the first excited state to order V0 is – (June – 2013)

Choices

Choice (4) Response
a.

V04(1±329π2)

b.

V04

c.

V04(1±649π2)

d.

V04(1±169π2)

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