# Quantum Mechanics-Eigenvalue Problems (CSIR (Council of Scientific & Industrial Research) Physical Sciences): Questions 6 - 10 of 11

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## Question number: 6

» Quantum Mechanics » Eigenvalue Problems

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Appeared in Year: 2014

MCQ▾

### Question

The Hamiltonian for a three – state quantum system is given by matrix, . When perturbed by where , the resulting shift in the energy eigenvalue is (December)

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question number: 7

» Quantum Mechanics » Eigenvalue Problems

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Appeared in Year: 2013

MCQ▾

### Question

If is the eigenfunction of a one – dimensional Hamiltonian with eigenvalue , the potential (in units where ) is – (Dec – 2013)

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question number: 8

» Quantum Mechanics » Eigenvalue Problems

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Appeared in Year: 2013

MCQ▾

### Question

A particle is prepared in a simultaneous eigenstate of and . If and are respectively the eigenvalues of and , then the expectation value of the particle in this state satisfies – (December -2013)

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question number: 9

» Quantum Mechanics » Eigenvalue Problems

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Appeared in Year: 2012

MCQ▾

### Question

Which of the following is a self – adjoint operator in the spherical polar coordinate system ? (June)

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question number: 10

» Quantum Mechanics » Eigenvalue Problems

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Appeared in Year: 2016

MCQ▾

### Question

Consider the two lowest normalised energy eigenfunction and of a one-dimensional system. They satisfy and , where is a real constant. The expectation value of the momentum operator in the state is: (December)

### Choices

Choice (4)Response

a.

0

b.

c.

d.

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