Quantum Mechanics-Eigenvalue Problems (CSIR Physical Sciences): Questions 1 - 4 of 9

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Question number: 1

» Quantum Mechanics » Eigenvalue Problems

Appeared in Year: 2013

MCQ▾

Question

The un – normalized wave function of a particle in a spherically symmetric potential is given by,

ψ(r)=zf(r)

Where, f(r) is a function of the radial variable r. The eigenvalue of the operator L2 (namely the square of the orbital angular momentum) is – (June)

Choices

Choice (4) Response

a.

2

b.

4

c.

2

d.

22

Question number: 2

» 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: 3

» Quantum Mechanics » Eigenvalue Problems

Appeared in Year: 2014

MCQ▾

Question

A particle of mass m in three dimensions is in the potential V(r)={ . Its ground state energy is - (June)

Choices

Choice (4) Response

a.

π22ma2

b.

3π222ma2

c.

π222ma2

d.

9π222ma2

Question number: 4

» Quantum Mechanics » Eigenvalue Problems

Appeared in Year: 2012

MCQ▾

Question

A particle of mass m is in a cubic box of size a . The potential inside the box (0xa,0ya,0za) is zero and infinite outside. If the particle is in an eigenstate of energy E=14π222ma2, its wavelength is – (June)

Choices

Choice (4) Response

a.

ψ=(2a)32sinπxasin2πyasin3πza

b.

ψ=(2a)32sin3πxasin5πyasin6πza

c.

ψ=(2a)32sin4πxasin8πyasin2πza

d.

ψ=(2a)32sin7πxasin4πyasin3πza

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