Quantum Mechanics (CSIR Physical Sciences): Questions 60 - 62 of 70

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Question number: 60

» Quantum Mechanics » Wave-Function in Coordinate Representations

Appeared in Year: 2012

MCQ▾

Question

The energy in the ground state and first excited state of a particle of mass m=12 in a potential V(x) are 4 and 1 , respectively, (in units in which =1 ). If the corresponding wave functions are related by ψ1(x)=ψ0(x)sinh(x) , then the ground state eigen function is – (December)

Choices

Choice (4) Response
a.

ψ0(x)=sech2x

b.

ψ0(x)=sechx

c.

ψ0(x)=sech3x

d.

ψ0(x)=sechx

Question number: 61

» Quantum Mechanics » Eigenvalue Problems

Appeared in Year: 2012

MCQ▾

Question

Which of the following is a self – adjoint operator in the spherical polar coordinate system (r,θ,ϕ) ? (June)

Choices

Choice (4) Response
a.

isinθθ

b.

isinθθ

c.

isin2θθ

d.

iθ

Question number: 62

» Quantum Mechanics » Variational Method

Appeared in Year: 2012

MCQ▾

Question

A variational calculation is done with the normalized trial wavefunction ψ(x)=154a52(a2x2) for the one dimensional potential well V(x)={0,if x a,if x >a , the ground state energy is estimated to be, (June)

Choices

Choice (4) Response
a.

322ma2

b.

524ma2

c.

533ma2

d.

325ma2

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