Quantum Mechanics-Motion in Central Potential (CSIR Physical Sciences): Questions 1 - 4 of 6

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Question number: 1

» Quantum Mechanics » Motion in Central Potential » Angular Momentum Algebra

Appeared in Year: 2013

MCQ▾

Question

A particle moves in a potential V=x2+y2+z22 . Which component (s) of the angular momentum is/are constant (s) of motion? (December)

Choices

Choice (4) Response

a.

OnlyLxandLy

b.

OnlyLz

c.

Lx,LyandLz

d.

Question does not provide sufficient data or is vague

Question number: 2

» Quantum Mechanics » Motion in Central Potential » Angular Momentum Algebra

Appeared in Year: 2014

MCQ▾

Question

Consider the normalized wavefunction ϕ=a1ψ11+a2ψ10+a3ψ11 ; where ψlm is a simultaneous normalized eigenfunction of the angular momentum operators L2 and Lz , with eigenvalue l(l+1)2 and m respectively. If ϕ is an eigenfunction of the operator Lx with eigenvalue , then - (December)

Choices

Choice (4) Response

a.

a1=a3=12,a2=12

b.

a1=a3=12,a2=12

c.

a1=a3=12,a2=12

d.

a1=a2=a3=13

Question number: 3

» Quantum Mechanics » Motion in Central Potential » Addition of Angular Momenta

Appeared in Year: 2011

MCQ▾

Question

The energy of the first excited quantum state of a particle in the two dimensional potential V(x,y)=12mω2(x2+4y2) is – (December)

Choices

Choice (4) Response

a.

3ω

b.

52ω

c.

32ω

d.

2ω

Question number: 4

» Quantum Mechanics » Motion in Central Potential » Angular Momentum Algebra

Appeared in Year: 2011

MCQ▾

Question

Consider a particle in a one dimensional potential that satisfies V(x)=V(x) . Let ψ0 and ψ1 denote the ground and the first excited states, respectively, and let ψ=α0 ψ0+α1 ψ1 be a normalized state with α0 and α1 being real constants. The expectation value x of the position operator x in the state ψ is given by, - (December)

Choices

Choice (4) Response

a.

α0α1[ψ0 x ψ1+ψ1 x ψ0]

b.

α02ψ0 x ψ0+α12ψ1 x ψ1

c.

α02+α12

d.

2α0α1

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