GATE PH 2025 Paper 1 — page 15

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

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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An electron with mass

and charge

is in the spin up state

at time

. A constant magnetic field is applied along the

-axis,

, where

is a constant. The Hamiltonian of the system is

, where

and

. The minimum time after which the electron will be in the spin down state along the

-axis, i.e.,

, is

Your answerChoose one option.

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2025 · Paper 1