GATE PH topic:quantum-mechanics PYQs & Answers — Page 2

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topic:quantum-mechanics

Questions 11–20 of 83. Imported answers require independent review unless marked reviewed.

Topic practice 83 questionsPage 2 of 9

Consider two operators

and

which are related as

. If

is a non-zero real number, which of the following statements is/are true?

Your answerSelect all correct options. You can choose more than one.

is Hermitian, then

is unitary.

is anti-Hermitian, then

is unitary.

is Hermitian, then

is anti-Hermitian, then

is Hermitian.

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Consider operators

, and

for three observables of a quantum system satisfying

, and

, with uncertainties

, respectively. From the options given below, which is/are implied by the commutation relations among

, and

Your answerSelect all correct options. You can choose more than one.

can be simultaneously diagonalized.

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The Hamiltonian of two interacting spin-1/2 particles is

, where

and

are the spin angular momenta of particles 1 and 2, respectively. Here,

eV. The energy in eV required to induce an excitation from the ground state to the excited state (rounded off to two decimal places) is ____

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A particle of mass

is in a potential

for

and

for

, where

is the angular frequency. The ratio of the energies corresponding to the lowest energy level to the next higher level is

Your answerChoose one option.

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A particle is scattered from a potential

, where

is a positive constant. Using the first Born approximation, the angular

dependence of differential scattering cross section

Your answerChoose one option.

Independent of

but dependent on

Dependent on

but independent of

Dependent on both

and

Independent of both

and

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Which one of the following is correct for the phase velocity

and group velocity

? (

is the speed of light in vacuum)

Your answerChoose one option.

For matter waves in the relativistic case,

For electromagnetic waves in a medium,

represents the speed with which energy propagates

For electromagnetic waves in a medium, both

and

can be more than

For matter waves in free space,

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Which of the following option(s) is/are correct for the ground state of a hydrogen atom?

Your answerSelect all correct options. You can choose more than one.

Linear Stark effect is zero

It has definite parity

Spin-orbit coupling is zero

Hyperfine splitting is zero

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Which of the following option(s) is/are correct for photons?

Your answerSelect all correct options. You can choose more than one.

Its rest mass is zero, but its energy is non-zero

It carries non-zero linear momentum

It carries zero spin angular momentum

It has two linearly independent states of polarization

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Let

and

denote the energy eigenstates of a one-dimensional simple harmonic oscillator. The position and momentum operators are

and

, respectively. The matrix element

is non-zero when

Your answerChoose one option.

only

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A two-level quantum system has energy eigenvalues

and

. A perturbing potential

is introduced, where

is a constant having dimensions of energy,

is a small dimensionless parameter, and

. The magnitudes of the first and the second order corrections to

due to

, respectively, are

Your answerChoose one option.

and

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GATE PH topic:quantum-mechanics PYQs

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