论文标题
突然加速电势中的量子颗粒
Quantum particles in a suddenly accelerating potential
论文作者
论文摘要
我们研究了在速度和/或加速度的多个突然变化下，量子粒子被困在一个维度中的量子粒子的行为。我们开发适当的形式主义来处理这种情况，并使用它来计算简单问题的过渡概率，例如无限盒中的粒子和简单的谐波振荡器。对于在两个和三个突然的速度变化下的无限长度$ l $的盒子，在初始速度和最终速度消失的情况下，我们发现该系统以$ΔT=τ_0\ equiv \ equiv \ equiv \ equiv \ frac {4ml^2} {π\ hbar} $ time time time time tire dies time time diestere（$Δ） 速度）。对于简单的谐波振荡器，我们发现通过突然改变（一个变化）获得的状态（一个变化）势最初在静态电势的特征状态下的粒子的速度和/或加速度为{\ sl sl cooherent}状态。对于加速度或速度的多次变化，我们发现哈密顿量的量子期望值与相应的经典期望值非常接近（可能是相同）。最后，粒子在加速谐波振荡器中的过渡概率（无突然的变化）与我们的形式主义计算出来，与Ludwig很久以前得出的公式一致，最近由Dodonov〜 \ cite {Dodonov21}进行了修改，但对无尺寸参数$γ$γ$γ$ umpersection {Dodonov21}一致。我们的可能性与$γ\ ll 1 $的参考〜\ cite {dodonov21}之一一致，但并非及时（单调衰减），这与参考文献中得出的结果相反。
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 $Δt = τ_0 \equiv \frac{4mL^2}{π\hbar}$, regardless of other parameters ($Δt$ 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 $γ$. Our probability agrees with the one of ref.~\cite{Dodonov21} for $γ\ll 1$ but is not periodic in time (it decays monotonously), contrary to the result derived in ref.~\cite{Dodonov21}.
