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The Schrödinger system H=-{1/2} (t_o/t)^a \partial_{xx} + (1/2) ω^2 (t/t_o)^b x^2
Michael Martin Nieto, D. Rodney Truax
We attack the specific time-dependent Hamiltonian problem H=-{1/2} (t_o/t)^a \partial_{xx} + (1/2) ω^2 (t/t_o)^b x^2. This corresponds to a time-dependent mass (TM) Schrödinger equ…
The Schrödinger system H=-{1/2}e^{Υ(t-t_o)}\partial_{xx} +\lfrac{1}{2}ω^2e^{-Υ(t-t_o)}x^2
Michael Martin Nieto, D. Rodney Truax
In this paper, we attack the specific time-dependent Hamiltonian problem H=-{1/2}e^{Υ(t-t_o)}\partial_{xx} +\lfrac{1}{2}ω^2e^{-Υ(t-t_o)}x^2. This corresponds to a time-dependent ma…
Schrödinger equations with time-dependent P^2 and X^2 terms
Michael Martin Nieto, D. Rodney Truax
We present some general results for the time-dependent mass Hamiltonian problem with H=-{1/2}e^{-2ν}\partial_{xx} +h^{(2)}(t)e^{2ν}x^2. This Hamiltonian corresponds to a time-depen…
Higher-Power Coherent and Squeezed States
Michael Martin Nieto, D. Rodney Truax
A closed form expression for the higher-power coherent states (eigenstates of ) is given. The cases j=3,4 are discussed in detail, including the time-evolution of the probab…
Electrons above a Helium Surface and the One-Dimensional Rydberg Atom
Michael Martin Nieto
Isolated electrons resting above a helium surface are predicted to have a bound spectrum corresponding to a one-dimensional hydrogen atom. But in fact, the observed spectrum is clo…