Quantum Mechanics (CSIR Physical Sciences): Questions 22 - 24 of 70

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Question number: 22

» Quantum Mechanics » Commutators and Heisenberg Uncertainty Principle

Appeared in Year: 2014

MCQ▾

Question

Suppose Hamiltonian of a conservative system in classical mechanics is H=ωxp ; where ω is a constant and x and p are the position and momentum respectively. The corresponding Hamiltonian in quantum mechanics, in the coordinate representation, is – (December)

Choices

Choice (4) Response

a.

iω(xx12)

b.

iωxx

c.

iω(xx+12)

d.

iω2xx

Question number: 23

» 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: 24

» 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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