GATE (Graduate Aptitude Test in Engineering) Physics: Questions 57 - 60 of 659

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Question number: 57

» Quantum Mechanics » Harmonic Oscillator

Appeared in Year: 2014

Short Answer Question▾

Write in Short

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 number: 58

» Quantum Mechanics » Linear Vectors and Operators in Hilbert Space

Appeared in Year: 2015

MCQ▾

Question

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.

Question number: 59

» Quantum Mechanics » Postulates of Quantum Mechanics

Appeared in Year: 2015

Short Answer Question▾

Write in Short

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 number: 60

» Mathematical Physics » Linear Differential Equations

Appeared in Year: 2015

MCQ▾

Question

A function satisfies the ordinary differential equation , where Consider the four statements P, Q, R, S as given below.

P: and are linearly independent solution for all values of

Q: and are linearly independent solution for all values of

R: and 1 are linearly independent solution for

S: and are linearly independent solution for all values of

The correct option for the combination of valid statements is –

Choices

Choice (4) Response

a.

P, R and S

b.

Q and R

c.

P and R

d.

R and S

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