GATE PH year:2024 PYQs & Answers — Page 7

Questions 61–65 of 65. Imported answers require independent review unless marked reviewed.

Topic practice 65 questionsPage 7 of 7

A particle of mass

in an infinite potential well of width

is subjected to a perturbation,

as shown in figure, where

is Planck’s constant.

The first order energy shift of the fourth energy eigenstate due to this perturbation is

The value of

is _____ (in integer).

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Consider a three-dimensional system of non-interacting bosons with zero chemical potential. The energy of the system

, where

is the wavevector. The low temperature specific heat of the system at constant volume depends on the temperature as

. The value of

is _____ (in integer).

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Consider the operational amplifier circuit shown in figure.

The output voltage

is ______ V (in integer).

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An electron in the Coulomb field of a proton is in the following state of coherent superposition of orthonormal states

Let

, and

represent the first three energy levels of the system. A sequence of measurements is done on the same system at different times. Energy is measured first at time

and the outcome is

. Then total angular momentum is measured at time

and finally energy is measured again at

. The probability of finding the system in a state with energy

after the final measurement is

. The value of

is _____ (in integer).

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According to the nuclear shell model, the absolute value of the difference in magnetic moments of

and

, in the units of nuclear magneton (

) is

. The magnitude of

is _____ (in integer).

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GATE PH year:2024 PYQs

Question 61

Question 62

Question 63

Question 64

Question 65