GATE (Graduate Aptitude Test in Engineering) Physics: Questions 364 - 367 of 659

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Question 364

Appeared in Year: 2009

Question

MCQ▾

and represent two physical characteristics of a quantum system. If is Hermitian, then for the product to be Hermitian, it is sufficient that –

Choices

Choice (4)Response

a.

is Hermitian and and commute

b.

is Hermitian

c.

is anti – Hermitian

d.

is Hermitian and and anti – commute

Question 365

Appeared in Year: 2009

Question

MCQ▾

The spin function of a free particle, in the basis in which is diagonal, can be written as and with eigenvalues and , respectively. In the given basis, the normalized eigen function of with eigenvalue

Choices

Choice (4)Response

a.

b.

c.

d.

Question 366

Appeared in Year: 2009

Question

MCQ▾

A particle is in the normalized state which is a superposition of the energy eigen states and . The average value of energy of the particle in the state is . The state is given by –

Choices

Choice (4)Response

a.

b.

c.

d.

Question 367

Appeared in Year: 2009

Question

MCQ▾

A classical particle is moving in an external potential field which is invariant under the following infinitesimal transformation –

Where is the matrix corresponding to rotation about the axis. The conserved quantities are (the symbols have their usual meaning)

Choices

Choice (4)Response

a.

b.

c.

d.

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