Quantum Mechanics-Eigenvalue Problems (CSIR Physical Sciences): Questions 5 - 8 of 9

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Question number: 5

» Quantum Mechanics » Eigenvalue Problems

Appeared in Year: 2012

MCQ▾

Question

Let ψnlm denote the eigenfunctions of a Hamiltonian for a spherically symmetric potential V(r) . The wave function ψ=14[ψ210+5ψ211+10ψ213] is an eigenfunction only of – (June)

Choices

Choice (4) Response

a.

L2andLz

b.

HandLz

c.

H,L2andLz

d.

HandL2

Question number: 6

» Quantum Mechanics » Eigenvalue Problems

Appeared in Year: 2014

MCQ▾

Question

The Hamiltonian H0 for a three – state quantum system is given by matrix, H0=(100020002) . When perturbed by H=ε(010101010); where ε1 , the resulting shift in the energy eigenvalue E0=2 is (December)

Choices

Choice (4) Response

a.

ε.2ε

b.

±ε

c.

±2ε

d.

ε,2ε

Question number: 7

» 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: 8

» 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

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