Quantum Mechanics (CSIR Physical Sciences): Questions 54 - 56 of 71

Get 1 year subscription: Access detailed explanations (illustrated with images and videos) to 401 questions. Access all new questions we will add tracking exam-pattern and syllabus changes. View Sample Explanation or View Features.

Rs. 300.00 or

Question number: 54

» Quantum Mechanics » Variational Method

Appeared in Year: 2013

MCQ▾

Question

The bound on the ground state energy of the Hamiltonian with an attractive delta – function potential, namely H=22md2dx2αδ(x)

Using the variational principle with the trial wavefunction ψ(x)=Aexp(bx2) is – [Given:0ettadt=Γ(a+1)] (June)

Choices

Choice (4) Response

a.

mα24π2

b.

mα25π2

c.

mα22π2

d.

mα2π2

Question number: 55

» Quantum Mechanics » Wave-Function in Momentum Representations

Appeared in Year: 2013

MCQ▾

Question

If ψnlm denotes the eigenfunction of the Hamiltonian with a potential V=V(r) , then the expectation value of the operator Lx2 and Ly2 in the state ψ=15(3ψ211+ψ21015ψ211) is – (June – 2013)

Choices

Choice (4) Response

a.

22

b.

3925

c.

26225

d.

13225

Question number: 56

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

Appeared in Year: 2013

MCQ▾

Question

The expectation value of the x – component of the orbital angular momentum Lx in the state, ψ=15[3ψ2, 1,1+5ψ2, 1,011ψ2, 1,+1]

(Where ψnlm are the eigenfunction in usual notation), is – (December -2013)

Choices

Choice (4) Response

a.

1025(11+3)

b.

2

c.

0

d.

1025(113)

Sign In