Quantum Mechanics-Variational Method (CSIR Physical Sciences): Questions 1 - 4 of 10

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Question number: 1

» Quantum Mechanics » Variational Method

Appeared in Year: 2014

MCQ▾

Question

Let ψnlm denote the eigenfunctions of a Hamiltonian for a spherically symmetric potential V (r). The expectation value of Lz in the state ψ=16[ψ200+5ψ210+10ψ211+20ψ211] is - (December)

Choices

Choice (4) Response

a.

518

b.

56

c.

518

d.

Question number: 2

» 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

Question number: 3

» Quantum Mechanics » Variational Method

Appeared in Year: 2011

MCQ▾

Question

If the perturbation H=ax , where a is a constant; is added to the infinite square well potential

V(x)={

The first order correction to ground state energy is: - (June)

Choices

Choice (4) Response

a.

aπ

b.

aπ4

c.

aπ2

d.

aπ2

Question number: 4

» Quantum Mechanics » Variational Method

Appeared in Year: 2013

MCQ▾

Question

A particle is in the ground state of an infinite square well potential given by,

V(x)={ The probability to find the particle in the interval between a2 and a2 is – (Dec- 2013)

Choices

Choice (4) Response

a.

12

b.

121π

c.

12+1π

d.

1π

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