Quantum Mechanics (CSIR Physical Sciences): Questions 37 - 39 of 71

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Question number: 37

» Quantum Mechanics » Motion in Central Potential » Angular Momentum Algebra

Appeared in Year: 2011

MCQ▾

Question

Consider a particle in a one dimensional potential that satisfies V(x)=V(x) . Let ψ0 and ψ1 denote the ground and the first excited states, respectively, and let ψ=α0 ψ0+α1 ψ1 be a normalized state with α0 and α1 being real constants. The expectation value x of the position operator x in the state ψ is given by, - (December)

Choices

Choice (4) Response

a.

α0α1[ψ0 x ψ1+ψ1 x ψ0]

b.

α02ψ0 x ψ0+α12ψ1 x ψ1

c.

α02+α12

d.

2α0α1

Question number: 38

» Quantum Mechanics » Spin-Statistics Connection

Appeared in Year: 2014

MCQ▾

Question

The effective spin – spin interaction between the electron spin Se and the proton spin Sp in the ground state of the Hydrogen atom is given by H=aSeSP . As a result of this interaction the energy levels split by an amount – (December)

Choices

Choice (4) Response

a.

32a2

b.

12a2

c.

2a2

d.

a2

Question number: 39

» Quantum Mechanics » Spin-Statistics Connection

Appeared in Year: 2014

MCQ▾

Question

Let, σ=(σ1,σ2,σ3); where σ1,σ2,σ3 are the Pauli matrices. If a and b are two arbitrary constant vectors in three dimensions, the commutator [aσ,bσ] is equal to (in the following I is the identity matrix). (December)

Choices

Choice (4) Response

a.

(ab)I

b.

(ab)(σ1+σ2+σ3)

c.

a b I

d.

2i(a×b)σ

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