Quantum particles in a suddenly accelerating potential
- URL: http://arxiv.org/abs/2206.01354v1
- Date: Fri, 3 Jun 2022 01:10:46 GMT
- Title: Quantum particles in a suddenly accelerating potential
- Authors: Paolo Amore, Francisco M. Fern\'andez, Jose Luis Valdez
- Abstract summary: We study the behavior of a quantum particle trapped in a confining potential in one dimension under multiple sudden changes of velocity and/or acceleration.
We develop the appropriate formalism to deal with such situation and we use it to calculate the probability of transition for simple problems such as the particle in an infinite box.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We study the behavior of a quantum particle trapped in a confining potential
in one dimension under multiple sudden changes of velocity and/or acceleration.
We develop the appropriate formalism to deal with such situation and we use it
to calculate the probability of transition for simple problems such as the
particle in an infinite box and the simple harmonic oscillator. For the
infinite box of length $L$ under two and three sudden changes of velocity,
where the initial and final velocity vanish, we find that the system undergoes
quantum revivals for $\Delta t = \tau_0 \equiv \frac{4mL^2}{\pi\hbar}$,
regardless of other parameters ($\Delta t$ is the time elapsed between the
first and last change of velocity). For the simple harmonic oscillator we find
that the states obtained by suddenly changing (one change) the velocity and/or
the acceleration of the potential, for a particle initially in an eigenstate of
the static potential, are {\sl coherent} states. For multiple changes of
acceleration or velocity we find that the quantum expectation value of the
Hamiltonian is remarkably close (possibly identical) to the corresponding
classical expectation values. Finally, the probability of transition for a
particle in an accelerating harmonic oscillator (no sudden changes) calculated
with our formalism agrees with the formula derived long time ago by Ludwig and
recently modified by Dodonov~\cite{Dodonov21}, but with a different expression
for the dimensionless parameter $\gamma$. Our probability agrees with the one
of ref.~\cite{Dodonov21} for $\gamma \ll 1$ but is not periodic in time (it
decays monotonously), contrary to the result derived in ref.~\cite{Dodonov21}.
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