Ok i think i have got this now:
\frac{d^2\psi}{dx^2}\,+\,\frac{2mE}{\hbar^2}\psi = 0
as you said: let:
k^2\,=\,\frac{2mE}{\hbar^2}
(1.) \frac{d^2\psi}{dx^2} = -k^2\psi
let:
\psi = e^mx
\frac{d\psi}{dx} = me^{mx}
\frac{d^2\psi}{dx^2} = m^2e^{mx}
Substitute into...
ordinary differential equations?
i can solve second order derivatives but only relatively simple ones. This is a bit above my head. Would you be able to point me in the right direction of what to start looking at to get the correct result?
Thanks for the reply so far.
Regards, Simon.
Homework Statement
Im doing an A-level project on the Schrödinger equation and am unsure on the mathematics used to obtain the following results:
The Schrödinger for a particle in no potential field (=0) has the solution:
psi(x)=e^ikx. i is defined below, I haven't really a clue as to...