Quantum Mechanics (GATE Physics): Questions 15 - 19 of 35

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Question number: 15

» Quantum Mechanics » Angular Momentum and Spin

Appeared in Year: 2014

Short Answer Question▾

Write in Short

ψ1 and ψ2 are two orthogonal states of a spin 12 system. It is given that

ψ1=13(10)+23(01) Where (10) and (01) represent the spin – up and spin – down states, respectively. When the system is in the state ψ2 , its probability to be in the spin – up state is _ .

Question number: 16

» Quantum Mechanics » Linear Vectors and Operators in Hilbert Space

Appeared in Year: 2016

MCQ▾

Question

If x and p are the x components of the position and the momentum operators of a particle respectively, the commutator [x2,p2] is –

Choices

Choice (4) Response
a.

2i(xppx)

b.

i(xp+px)

c.

i(xppx)

d.

2i(xp+px)

Passage

The wave function of a particle moving in free space is given by, ψ=eikx+2eikx

Question number: 17 (1 of 2 Based on Passage) Show Passage

» Quantum Mechanics » Schrodinger Equation

Appeared in Year: 2012

MCQ▾

Question

The energy of the particle is –

Choices

Choice (4) Response
a.

52k22m

b.

2k2m

c.

2k22m

d.

32k24m

Question number: 18 (2 of 2 Based on Passage) Show Passage

» Quantum Mechanics » Postulates of Quantum Mechanics

Appeared in Year: 2012

MCQ▾

Question

The probability current density for the real part of the wavefunction is –

Choices

Choice (4) Response
a.

km

b.

0

c.

1

d.

k2m

Question number: 19

» Quantum Mechanics » One, Two and Three-Dimensional Potential Problems

Appeared in Year: 2012

MCQ▾

Question

A particle of mass m is confined in a two dimensional square well potential of dimension a . This potential V(x,y) is given by,

V(x,y)={0,fora<x<aanda<y<a,elsewhere

The energy of the first excited state for this particle is given by,

Choices

Choice (4) Response
a.

5π222ma

b.

4π22ma2

c.

2π22ma2

d.

π22ma2

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