Quantum Mechanics-Linear Vectors and Operators in Hilbert Space [GATE (Graduate Aptitude Test in Engineering) Physics (PE)]: Questions 1 - 6 of 15

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Question 1

Appeared in Year: 2013

Question MCQ▾

Consider the normalized state of a particle in a one – dimensional harmonic oscillator:

Where and denoted the ground and first excited states respectively, and b1 and b2 are real constants. The expectation value of the displacement in the state will be a minimum when – (June)

Choices

Choice (4)Response

a.

b.

c.

d.

Edit

Question 2

Appeared in Year: 2014

Question MCQ▾

Let and denoted the normalized eigenstate of a particle with energy eigenvalue and respectively, with . At time the particle is prepared in a state . The shortest time T at which will be orthogonal to is – (December)

Choices

Choice (4)Response

a.

b.

c.

d.

Edit

Question 3

Appeared in Year: 2016

Question MCQ▾

are the Pauli matrices. The expression is equal to –

Choices

Choice (4)Response

a.

b.

c.

d.

Edit

Question 4

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.

Edit

Question 5

Appeared in Year: 2016

Question MCQ▾

Which of the following operators is Hermitian?

Choices

Choice (4)Response

a.

b.

c.

d.

Edit

Question 6

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.

Edit