Quantum Mechanics-Timeindependent Perturbation Theory and Applications (CSIR Physical Sciences): Questions 1 - 3 of 8

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Question number: 1

» Quantum Mechanics » Timeindependent Perturbation Theory and Applications

Appeared in Year: 2012

MCQ▾

Question

The energy eigen values of a particle in the potential V(x)=12mω2x2ax are – (December)

Choices

Choice (4) Response

a.

En=(n+12)ωa2mω2

b.

En=(n+12)ω+a22mω2

c.

En=(n+12)ω

d.

En=(n+12)ωa22mω2

Question number: 2

» Quantum Mechanics » Timeindependent Perturbation Theory and Applications

Appeared in Year: 2013

MCQ▾

Question

The motion of a particle of mass m in one dimension is described by the Hamiltonian H=p22m+12mω2x2+λx . What is the difference between the (quantized) energy of the first two levels? (In the following, x is the expectation value of x in the ground state. )

Choices

Choice (4) Response

a.

ω+λx

b.

ω+λ22mω2

c.

ω

d.

ωλx

Question number: 3

» Quantum Mechanics » Timeindependent Perturbation Theory and Applications

Appeared in Year: 2011

MCQ▾

Question

The perturbation H=bx4 , where b is a constant, is added to the one dimensional harmonic oscillator potential V(x)=12mω2x2 . Which of the following denotes the correction to the ground state energy to first order in b?

Hint: The normalized ground state wave function of the one dimensional harmonic oscillator potential is ψ=(mωπ)14emωx22 . You may use the following integral

x2neax2dx=an12Γ(n+12)

(December)

Choices

Choice (4) Response

a.

15b24m2ω2

b.

3b24m2ω2

c.

3b22m2ω2

d.

3b22πm2ω2

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