# Quantum Mechanics [GATE (Graduate Aptitude Test in Engineering) Physics]: Questions 6 - 12 of 80

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## Question 6

Appeared in Year: *2015*

### Write in Short

Short Answer▾The Pauli matrices for three spin particles are , respectively. The dimension of the Hilbert space required to define an operator is –

## Question 7

Appeared in Year: *2016*

### Question

MCQ▾are the Pauli matrices. The expression is equal to –

### Choices

Choice (4) | Response | |
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a. | ||

b. | ||

c. | ||

d. |

## Question 8

Appeared in Year: *2014*

### Write in Short

Short Answer▾A one dimensional harmonic oscillator is in the superposition of number states, , given by

The average energy of the oscillator in the given state is .

## Question 9

Appeared in Year: *2015*

### Question

MCQ▾An operator for a spin particle is given by , where denotes Pauli matrices and is a constant. The eigenvalue of are –

### Choices

Choice (4) | Response | |
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a. | ||

b. | ||

c. | ||

d. |

## Question 10

Appeared in Year: *2015*

### Write in Short

Short Answer▾Consider a system of eight non – interacting, identical quantum particle of spin in a one dimensional box of length L. The minimum excitation energy of the system, in units of is ________

## Question 11

Appeared in Year: *2016*

### Question

MCQ▾Which of the following operators is Hermitian?

### Choices

Choice (4) | Response | |
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a. | ||

b. | ||

c. | ||

d. |

## Question 12

Appeared in Year: *2015*

### Question

MCQ▾Let L and p be the angular and linear momentum operates, respectively for a particle. The commutator gives –

### Choices

Choice (4) | Response | |
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a. | ||

b. | 0 | |

c. | ||

d. |