# 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

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## 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,

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### 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)

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 –

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## Question 35 (2 of 2 Based on Passage)

Appeared in Year: *2011*

### Question

MCQ▾The value of for which is orthogonal to is –

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## Question 36

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 –

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## Question 37

### Question

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

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