Quantum Mechanics (CSIR (Council of Scientific & Industrial Research) Physical Sciences): Questions 37 - 39 of 80

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Question number: 37

» Quantum Mechanics » Motion in Central Potential » Angular Momentum Algebra

Appeared in Year: 2011

MCQ▾

Question

Consider a particle in a one dimensional potential that satisfiesEquation . Let Equation and Equation denote the ground and the first excited states, respectively, and let Equation be a normalized state with Equation and Equation being real constants. The expectation value Equation of the position operator Equation in the state Equation is given by, - (December)

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

Equation

Question number: 38

» Quantum Mechanics » Spin-Statistics Connection

Appeared in Year: 2014

MCQ▾

Question

The effective spin – spin interaction between the electron spin Equation and the proton spin Equation in the ground state of the Hydrogen atom is given by Equation . As a result of this interaction the energy levels split by an amount – (December)

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

Equation

Question number: 39

» Quantum Mechanics » Spin-Statistics Connection

Appeared in Year: 2014

MCQ▾

Question

Let, Equation where Equation are the Pauli matrices. If Equation and Equation are two arbitrary constant vectors in three dimensions, the commutator Equation is equal to (in the following I is the identity matrix). (December)

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

Equation

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