Quantum Mechanics [GATE (Graduate Aptitude Test in Engineering) Physics]: Questions 32 - 37 of 80

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Question 32

Appeared in Year: 2011

Question

MCQ▾

The normalized ground state wavefunction of a hydrogen atom is given by,

Where is the Bohr radius and is the distance of the electron from the nucleus, located at the origin. The expectation value is

Choices

Choice (4)Response

a.

b.

c.

d.

Question 33

Appeared in Year: 2011

Question

MCQ▾

The quantum mechanical operator for the moment of a particle moving in one dimension is given by,

Choices

Choice (4)Response

a.

b.

c.

d.

Passage

In a one – dimensional harmonic oscillator, and are respectively the ground, first and the second excited states. These three states are normalized and are orthogonal to one another.

, where is a constant.

Question 34 (1 of 2 Based on Passage)

Quantum Mechanics

Appeared in Year: 2011

Question

MCQ▾

For the value of determined in above question, the expectation value of energy of the oscillator in the state is –

Choices

Choice (4)Response

a.

b.

c.

d.

Question 35 (2 of 2 Based on Passage)

Quantum Mechanics

Appeared in Year: 2011

Question

MCQ▾

The value of for which is orthogonal to is –

Choices

Choice (4)Response

a.

1

b.

c.

d.

2

Question 36

Quantum Mechanics

Appeared in Year: 2010

Question

MCQ▾

A particle of mass is confined in the potential ,

Let the wavefunction of the particle be given by , where and are the eigenfunctions of the ground state and the first excited state respectively. The expectation value of the energy is –

Potential V/S Position Graph

Choices

Choice (4)Response

a.

b.

c.

d.

Question 37

Quantum Mechanics

Question

MCQ▾

For a spin particle, in the eigen basis of the expectation value is –

Choices

Choice (4)Response

a.

b.

c.

d.

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