Quantum Mechanics (CSIR Physical Sciences): Questions 14 - 17 of 70

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Question number: 14

» Quantum Mechanics » Spin-Orbit Coupling

Appeared in Year: 2012

MCQ▾

Question

The minimum energy of a collection of 6 non – interacting electrons of spin 12 and mass m placed in a one dimensional infinite square well potential of width L is – (December)

Choices

Choice (4) Response

a.

91π22mL2

b.

7π22mL2

c.

3π22mL2

d.

14π22mL2

Question number: 15

» Quantum Mechanics » Commutators and Heisenberg Uncertainty Principle

Appeared in Year: 2012

MCQ▾

Question

Given the usual canonical commutation relation, the commutator [A,B] of A=i(xpyypx) and B=(ypz+zpy) is - (December)

Choices

Choice (4) Response

a.

(xpzpxz)

b.

(xpzpxz)

c.

(xpz+pxz)

d.

(xpz+pxz)

Question number: 16

» Quantum Mechanics » Commutators and Heisenberg Uncertainty Principle

Appeared in Year: 2014

MCQ▾

Question

Let x and p denote, respectively, the coordinate and momentum operators satisfying the canonical commutation relation [x,p]=i in natural units (=1) . Then the commutator [x,pep] is – (December)

Choices

Choice (4) Response

a.

ipep

b.

i(1p)ep

c.

i(1ep)

d.

i(1p2)ep

Question number: 17

» Quantum Mechanics » Variational Method

Appeared in Year: 2012

MCQ▾

Question

The wave function of a state of the hydrogen atom is given by,

ψ=ψ200+2ψ211+3ψ210+2ψ211

Where, ψnlm is the normalized eigen function of the state with quantum numbers n, l and m in the usual notation. The expectation value of Lz is the state ψ is – (December)

Choices

Choice (4) Response

a.

1116

b.

38

c.

8

d.

1516

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