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dats13
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Homework Statement
The quaestion asks to determine the ground an first excited state of the wavefuntion of a particle in a 1-D potential given by [tex]V(x)=B\left | x \right |[/tex].
Homework Equations
The Time Independent Schrodinger Equation (TISE):
[tex]-\frac{\hbar}{2m}\frac{d^{2}\Psi }{dx^{2}}+V\Psi=E\Psi[/tex]
The Attempt at a Solution
I substituted the potential into the TISE and with some rearraging of terms I get the following differential equation.
[tex] {\Psi}''+\frac{2m}{\hbar^{2}}(E-B\left | x \right |)\Psi=0[/tex]
This is where I'm stuck. I don't know how to solve this equation because of the potential is dependent on [tex]x[/tex]. Any suggestions would be greatly appreciated.