- #1
Just some guy
- 69
- 1
I'm currently reading up about solving the schrodinger equation for a one-dimensional particle in a one-dimensional box with an infinite level of potential outside the box, and I have a *slight* problem (no, really, it is very slight)
I've got to the equation where the Wavefunction = Acos(2*x*pi/lambda - omega*t). And the text I'm working on says that using the Planck relationship omega is equal to energy? ey! I was under the impression that omega equalled angular velocity (not that I have a clue why a wave would have angular velocity, but that's another story).
Besides, I'm not entirely sure how that equation is in the form it is - the wave equation arrived at by modelling a traveling 1-d wave comes to Asin(2*pi/lambda(x ± vt). Firstly, how does that get to a cos expression (is that just coming from using different initial conditions where in the first case x = A at t = 0 (well, psi, or whatever) and x = 0 at t = 0 in the second? That leaves the omega*t bit of the first equation - I'm assuming that is equivalent to 2*pi*vt/lambda from the traveling wave equation - how do those two relate?
And finally where did the minus sign go from the second equation?
Blech, sorry for the convoluted post, I'm not really this confused! honest!
Cheers,
Just some guy
I've got to the equation where the Wavefunction = Acos(2*x*pi/lambda - omega*t). And the text I'm working on says that using the Planck relationship omega is equal to energy? ey! I was under the impression that omega equalled angular velocity (not that I have a clue why a wave would have angular velocity, but that's another story).
Besides, I'm not entirely sure how that equation is in the form it is - the wave equation arrived at by modelling a traveling 1-d wave comes to Asin(2*pi/lambda(x ± vt). Firstly, how does that get to a cos expression (is that just coming from using different initial conditions where in the first case x = A at t = 0 (well, psi, or whatever) and x = 0 at t = 0 in the second? That leaves the omega*t bit of the first equation - I'm assuming that is equivalent to 2*pi*vt/lambda from the traveling wave equation - how do those two relate?
And finally where did the minus sign go from the second equation?
Blech, sorry for the convoluted post, I'm not really this confused! honest!
Cheers,
Just some guy