# Quantum Mechanics-Variational Method (CSIR (Council of Scientific & Industrial Research) Physical Sciences): Questions 1 - 5 of 11

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## Question number: 1

» Quantum Mechanics » Variational Method

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Appeared in Year: 2014

MCQ▾

### Question

Let denote the eigenfunctions of a Hamiltonian for a spherically symmetric potential V (r). The expectation value of in the state is - (December)

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question number: 2

» Quantum Mechanics » Variational Method

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Appeared in Year: 2012

MCQ▾

### Question

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

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

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question number: 3

» Quantum Mechanics » Variational Method

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Appeared in Year: 2011

MCQ▾

### Question

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

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

### Choices

Choice (4)Response

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b.

c.

d.

## Question number: 4

» Quantum Mechanics » Variational Method

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Appeared in Year: 2013

MCQ▾

### Question

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

The probability to find the particle in the interval between and is – (Dec- 2013)

### Choices

Choice (4)Response

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b.

c.

d.

## Question number: 5

» Quantum Mechanics » Variational Method

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Appeared in Year: 2013

MCQ▾

### Question

The bound on the ground state energy of the Hamiltonian with an attractive delta – function potential, namely

Using the variational principle with the trial wavefunction is – (June)

### Choices

Choice (4)Response

a.

b.

c.

d.

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