Quantum Mechanics (CSIR Physical Sciences): Questions 5 - 7 of 71

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Question number: 5

» Quantum Mechanics » Variational Method

Appeared in Year: 2014

MCQ▾

Question

Let ψnlm denote the eigenfunctions of a Hamiltonian for a spherically symmetric potential V (r). The expectation value of Lz in the state ψ=16[ψ200+5ψ210+10ψ211+20ψ211] is - (December)

Choices

Choice (4) Response

a.

518

b.

56

c.

518

d.

Question number: 6

» Quantum Mechanics » Eigenvalue Problems

Appeared in Year: 2014

MCQ▾

Question

A particle of mass m in the potential V(x,y)=12mω2(4x2+y2), is in an eigenstate of energy E=52ω . The corresponding unnormalized eigenfunction is – (June)

Choices

Choice (4) Response

a.

yexp[mω2(x2+y2)]

b.

yexp[mω2(2x2+y2)]

c.

xyexp[mω2(x2+y2)]

d.

xexp[mω2(2x2+y2)]

Question number: 7

» Quantum Mechanics » Dirac Notation for State Vectors

Appeared in Year: 2014

MCQ▾

Question

Let ψ1 and ψ2 denoted the normalized eigenstate of a particle with energy eigenvalue E1 and E2 respectively, with E2>E1 . At time t=0 the particle is prepared in a state ψ(t=0)=12(ψ1+ψ2) . The shortest time T at which ψ(t=T) will be orthogonal to ψ(t=0) is – (December)

Choices

Choice (4) Response

a.

π4(E2E1)

b.

2πE2E1

c.

π2(E2E1)

d.

πE2E1

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