Time evolution of the ladder operators
Not what you're looking for?
The evolution operator U(t,0) of a one-dimensional harmonic oscillator is written:
U(t,0) = e^(-iHt/h)
with:
H = hw(a^t*a + 1/2)
Consider the operators:
a(t) = U^t(t,0) a U(t,0)
a^t(t) = U^t(t,0) a^t U(t,0)
By calculating their action on the eigenkets | phi(n) > of H, find the expression for a(t) and a^t(t) in terms of a and a^t.
See attached file for question in proper mathematical format.
Purchase this Solution
Solution Summary
The solution shows how to calculate the time evolution of the ladder operators of the simple harmonic oscillator.
Solution Preview
Hello and thank you for posting your question to Brainmass.
The solution is attached below in two files. the files are identical in content, only differ in format. The ...
Purchase this Solution
Free BrainMass Quizzes
Intro to the Physics Waves
Some short-answer questions involving the basic vocabulary of string, sound, and water waves.
Classical Mechanics
This quiz is designed to test and improve your knowledge on Classical Mechanics.
Basic Physics
This quiz will test your knowledge about basic Physics.
Introduction to Nanotechnology/Nanomaterials
This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.
Variables in Science Experiments
How well do you understand variables? Test your knowledge of independent (manipulated), dependent (responding), and controlled variables with this 10 question quiz.