Physics
2019 · Paper 1
Take it one question at a time. Try an answer, then check your understanding.
Complete GATE PH 2019 Paper 1 overview, original pages and practice · Timed previous-paper practice
Questions 31–33 of 65. Imported answers require review unless explicitly marked reviewed.
Question 21
Open questionPHNAT1 markNeeds review
The Hamiltonian for a quantum harmonic oscillator of mass
in three dimensions is
where
is the angular frequency. The expectation value of
in the first excited state of the oscillator in units of
(rounded off to one decimal place) isLog in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 22
Open questionPHNAT1 markNeeds review
The Hamiltonian for a particle of mass
is
where
and
are the generalized coordinate and momentum, respectively,
is time and
is a constant. For the initial condition,
and
at
,
. The value of
isLog in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 23
Open questionPHNAT1 markNeeds review
At temperature
Kelvin (K), the value of the Fermi function at an energy 0.5 eV above the Fermi energy is 0.01. Then,
, to the nearest integer, is
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer