# Quantum Mechanics-Linear Vectors and Operators in Hilbert Space [GATE (Graduate Aptitude Test in Engineering) Physics]: Questions 1 - 6 of 10

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## Question 1

Appeared in Year: 2016

### Question MCQ▾

are the Pauli matrices. The expression is equal to –

### Choices

Choice (4)Response

a.

b.

c.

d.

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## Question 2

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

a.

b.

c.

d.

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## Question 3

Appeared in Year: 2016

### Question MCQ▾

Which of the following operators is Hermitian?

### Choices

Choice (4)Response

a.

b.

c.

d.

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## Question 4

Appeared in Year: 2016

### Question MCQ▾

If and are the components of the position and the momentum operators of a particle respectively, the commutator is –

### Choices

Choice (4)Response

a.

b.

c.

d.

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## Question 5

Appeared in Year: 2013

### Question MCQ▾

Which one of the following commutation relation is NOT CORRECT? Here, symbols have their usual meanings.

### Choices

Choice (4)Response

a.

b.

c.

d.

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## Question 6

Appeared in Year: 2013

### Write in Short Short Answer▾

A spin – half particle is in a linear superposition of its spin – up and spin – down states. If and are the eigenstate of then what is the expectation value, up to one decimal place, of the operator ? Here, symbols have their usual meaning.

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