Time evolution of a superposition of two energy eigenstates
Not what you're looking for?
See the attached file.
Purchase this Solution
Solution Summary
A detailed solution is given regarding time evolution of a superposition of two energy eigenstates.
Solution Preview
The Schrödinger equation is:
i hbar d|psi>/dt = H|psi> (1)
The initial state is:
|psi(t=0)> = N(|1> + |2>)
where |1> and |2> are two eigenstates of the Hamiltonian:
H|1> = E1 |1>
H|2> = E2 |2>
And E1 is not equal to E2 (by definition as the two states are nondegenerate)
The normalization constant N = 1/sqrt(2) is |1> and |2> are normalized.
We can solve Eq. (1) as follows. Since the equation is a linear differential equation, a superposition of two solutions is another solution. Such a superposition will satisfy the superposition of the initial conditions of the individual solutions. Now, we can write any state as a superposition of eigenstates of the Hamiltonian. So, all we need to do is to solve Eq. (1) for the initial condition were ...
Purchase this Solution
Free BrainMass Quizzes
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.
Intro to the Physics Waves
Some short-answer questions involving the basic vocabulary of string, sound, and water waves.
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.
Classical Mechanics
This quiz is designed to test and improve your knowledge on Classical Mechanics.
The Moon
Test your knowledge of moon phases and movement.