I am asked to determine the expressions for coefficients of the solutions [tex]\psi_1[/tex] and [tex] \psi_2 [/tex] to the Schrodinger's Equation in a system where a particle travelling to the right encounters a potential step when [tex] E < V_0 [/tex], where E is the total energy.(adsbygoogle = window.adsbygoogle || []).push({});

What I was able to come up with is that

[tex]

\psi_1 = Ae^{kx} + Be^{-kx}, k = \frac{\sqrt{2mE}}{\hbar}

[/tex]

[tex]

\psi_2 = Ce^{qx} + De^{-qx}, q = \frac{\sqrt{2m(E-V_0)}}{\hbar}

[/tex]

What I also know is that [tex]Ce^{qx}[/tex] is unacceptable because the wave must decay exponentially when it hits the barrier.

My first question is whether or not this statement is true:

[tex]

\int_{-\infty}^{0}|\psi_1|^2dx + \int_{0}^{+\infty}|\psi_2|^2dx = 1

[/tex]

My second question is if [tex]Be^{-kx}[/tex] is an acceptable solution to [tex]\psi_1[/tex]. In my opinion i believe it is not acceptable because it diverges as x negative approaches infinity.

Thanks for any help.

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# Homework Help: Quantum Mechanics Problem

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