Quantum Mechanics (CSIR Physical Sciences): Questions 28 - 30 of 70

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Question number: 28

» Quantum Mechanics » Commutators and Heisenberg Uncertainty Principle

Appeared in Year: 2014

MCQ▾

Question

The matrices A=[010100000],B=[001000000]andC=[000001000] Satisfy the commutation relations (June)

Choices

Choice (4) Response

a.

[A,B]=B,[B,C]=0,[C,A]=A

b.

[A,B]=C,[B,C]=A,[C,A]=B

c.

[A,B]=C,[B,C]=0,[C,A]=B

d.

[A,B]=B+C,[B,C]=0,[C,A]=B+C

Question number: 29

» 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

Question number: 30

» Quantum Mechanics » Motion in Central Potential » Addition of Angular Momenta

Appeared in Year: 2011

MCQ▾

Question

The energy of the first excited quantum state of a particle in the two dimensional potential V(x,y)=12mω2(x2+4y2) is – (December)

Choices

Choice (4) Response

a.

3ω

b.

52ω

c.

32ω

d.

2ω

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