Quantum Mechanics (CSIR Physical Sciences): Questions 34 - 36 of 71

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Question number: 34

» Quantum Mechanics » WKB Approximation

Appeared in Year: 2014

MCQ▾

Question

Consider a particle of mass m in the potential V(x)=a x ,a>0 . The energy eigenvalues En(n=0, 1,2,) , in the WKB approximation, are – (December)

Choices

Choice (4) Response

a.

[3aπ42m(n+12)]43

b.

3aπ42m(n+12)

c.

[3aπ42m(n+12)]23

d.

[3aπ42m(n+12)]13

Question number: 35

» Quantum Mechanics » Spin-Statistics Connection

Appeared in Year: 2011

MCQ▾

Question

The Hamiltonian of an electron in a constant magnetic field B is given by H=μσB where μ is a positive constant and σ=(σ1,σ2,σ3) denotes the Pauli matrices. Let ω=μB and I be the 2×2 unit matrix. Then the operator eiHt simplifies to – (June)

Choices

Choice (4) Response

a.

Icosωt+iσBBsinωt

b.

Isin2ωt+iσBBcos2ωt

c.

Icosωt2+iσBBsinωt2

d.

Isinωt+iσBBcosωt

Question number: 36

» Quantum Mechanics » Relativistic Quantum Mechanics » Dirac Equations

Appeared in Year: 2014

MCQ▾

Question

The ground state energy of the attractive delta function potential V(x)=bδ(x) ; where b>0 , is calculated with the variational trial function ψ(x)={Acos(πx2a),(fora<x<a)0,(otherwise); is (December)

Choices

Choice (4) Response

a.

mb2π22

b.

mb24π22

c.

mb22π22

d.

2mb2π22

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