Quantum Mechanics (CSIR Physical Sciences): Questions 25 - 27 of 71

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Question number: 25

» Quantum Mechanics » Eigenvalue Problems

Appeared in Year: 2012

MCQ▾

Question

Let ψnlm denote the eigenfunctions of a Hamiltonian for a spherically symmetric potential V(r) . The wave function ψ=14[ψ210+5ψ211+10ψ213] is an eigenfunction only of – (June)

Choices

Choice (4) Response

a.

L2andLz

b.

HandLz

c.

H,L2andLz

d.

HandL2

Question number: 26

» Quantum Mechanics » Eigenvalue Problems

Appeared in Year: 2014

MCQ▾

Question

The Hamiltonian H0 for a three – state quantum system is given by matrix, H0=(100020002) . When perturbed by H=ε(010101010); where ε1 , the resulting shift in the energy eigenvalue E0=2 is (December)

Choices

Choice (4) Response

a.

ε.2ε

b.

±ε

c.

±2ε

d.

ε,2ε

Question number: 27

» Quantum Mechanics » Wave-Function in Coordinate Representations

Appeared in Year: 2011

MCQ▾

Question

The wavefunction of a particle is given is given by ψ=(12ϕ0+iϕ1) , where ϕ0 and ϕ1 are the normalized eigenfunctions with energies E0 and E1 corresponding to the ground state and first excited state, respectively. The expectation value of the Hamiltonian in state ψ is –

(June)

Choices

Choice (4) Response

a.

E02+E1

b.

E02E13

c.

E0+2E13

d.

E02E1

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