Quantum Mechanics-Linear Vectors and Operators in Hilbert Space (GATE Physics): Questions 1 - 5 of 6

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Question number: 1

» Quantum Mechanics » Linear Vectors and Operators in Hilbert Space

Appeared in Year: 2016

MCQ▾

Question

σx,σyandσz are the Pauli matrices. The expression 2σxσy+σyσx is equal to –

Choices

Choice (4) Response

a.

iσz

b.

3iσz

c.

3iσz

d.

iσz

Question number: 2

» Quantum Mechanics » Linear Vectors and Operators in Hilbert Space

Appeared in Year: 2015

MCQ▾

Question

An operator for a spin 12 particle is given by A^=λσB , where B=B2(x^+y^), σ denotes Pauli matrices and λ is a constant. The eigenvalue of A^ are –

Choices

Choice (4) Response

a.

0,λB

b.

±λB

c.

0,λB

d.

±λB2

Question number: 3

» Quantum Mechanics » Linear Vectors and Operators in Hilbert Space

Appeared in Year: 2016

MCQ▾

Question

Which of the following operators is Hermitian?

Choices

Choice (4) Response

a.

id2dx2

b.

ddx

c.

d3dx3

d.

d2dx2

Question number: 4

» 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)

Question number: 5

» Quantum Mechanics » Linear Vectors and Operators in Hilbert Space

Appeared in Year: 2013

MCQ▾

Question

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

Choices

Choice (4) Response

a.

[L2,Lz]=0

b.

[Lx,Ly]=iLz

c.

[Lz,L+]=L+

d.

[Lz,L]=L

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