CSIR Physical Sciences: Questions 138 - 140 of 401

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Question number: 138

» Classical Mechanics » Lagrangian and Hamiltonian Formalism and Equations of Motion

Appeared in Year: 2014

MCQ▾

Question

The equation of motion of a system described by the time dependent Lagrangian L=eγt[12mx˙2V(x)] is – (December)

Choices

Choice (4) Response

a.

mx¨+γmx˙+dVdx=0

b.

mx¨+dVdx=0

c.

mx¨+γmx˙dVdx=0

d.

mx¨γmx˙+dVdx=0

Question number: 139

» 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: 140

» 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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