GATE PH concept:one-dimensional-potentials PYQs & Answers

Questions 1–3 of 3. Imported answers require independent review unless marked reviewed.

A system of five identical, non-interacting particles with mass

and spin

is confined to a one-dimensional potential well of length

. If the lowest energy of the system is

, the value of

(in integer) is _____.

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The wavefunction of a particle in an infinite one-dimensional potential well at time

where

and

are the normalized ground state, the normalized first excited state and the normalized second excited state, respectively.

and

are the eigen-energies corresponding to

and

, respectively. The expectation value of energy of the particle in state

Your answerChoose one option.

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Consider a one-dimensional potential well of width

. Using the uncertainty principle

, an estimate of the minimum depth of the well such that it has at least one bound state for an electron is

Your answerChoose one option.

1 μeV

1 meV

1 eV

1 MeV

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GATE PH concept:one-dimensional-potentials PYQs