GATE PH 2021 Paper 1 — page 15

Questions 43–45 of 65. Imported answers require review unless explicitly marked reviewed.

Consider a system of three distinguishable particles, each having spin

such that

with corresponding magnetic moments

. When the system is placed in an external magnetic field

pointing along the z-axis, the total energy of the system is

. Let

be the state where the first spin has

. The probability of having the state

and the mean magnetic moment (in the +z direction) of the system in state

are

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Consider a particle in a one-dimensional infinite potential well with its walls at

and

. The system is perturbed as shown in the figure.

The first order correction to the energy eigenvalue is

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Consider a state described by

, where

and

are respectively the second and fourth normalized harmonic oscillator wave functions and

is the angular frequency of the harmonic oscillator. The wave function

will be orthogonal to

at time

equal to

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2021 · Paper 1