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

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## Question number: 6

» Quantum Mechanics » Variational Method

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Appeared in Year: 2012

MCQ▾

### Question

What would be the ground state energy of the Hamiltonian – If variational principle is used to estimate it with the trial wavefunction with b, as the variational parameter?

(December)

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question number: 7

» Quantum Mechanics » Variational Method

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Appeared in Year: 2012

MCQ▾

### Question

A variational calculation is done with the normalized trial wavefunction for the one dimensional potential well , the ground state energy is estimated to be, (June)

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question number: 8

» Quantum Mechanics » Variational Method

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MCQ▾

### Question

Let and denote the normalized eigenstate corresponding to the ground and first excited state of a one dimensional harmonic oscillator. The uncertainty in the state is:

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question number: 9

» Quantum Mechanics » Variational Method

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Appeared in Year: 2011

MCQ▾

### Question

The wave function of the particle at time is given by , where and are the normalized eigen states with eigen values and respectively, . The shortest time after which will become orthogonal to is – (December)

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question number: 10

» Quantum Mechanics » Variational Method

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Appeared in Year: 2011

MCQ▾

### Question

If an electron is in the ground state of the hydrogen atom, the probability that its distance from the proton is more than one Bohr radius is approximately, (June)

### Choices

Choice (4)Response

a.

0.68

b.

0.91

c.

0.48

d.

0.28

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