Shrodinger Equation help

[shrugBERT]

Homework Statement

A particle of mass m in confined in a 1 dimensional box with origin at the center. the box extends from -a/2 to a/2 the potential energy is v(x) = 0 where -a/2<x< a/2 and infinite when x > a/2.

I have to write the shrodinger equation for the outside and inside of the box, solve the equation for inside the box in the form of wavefunc = A sin (cx) + B cos (cx). Give a rule determining all possible values of C and for each possible c determined give the conditions the constants A and B must adhere to to make the wavefunction a satisfactory solution to the shrodinger EQ

and last but not least express the energy in terms of C.

Homework Equations

H psi = E psi
h bar (used down below) = h/2pi
edit: oh i also used L instead of a for a variable when talking about the length of the box

The Attempt at a Solution

S.E. for particle outside box

psi(x) = sqrt(2/L) sin (n pi x)/L

S.E. for particle inside box

(-h bar^2)/2m + d psi/dx^2 = i(h bar) d psi/dt


solution to S.E for particle inside a box

Psi (x,t) = Ae^(i2pi/lamda - omega t) ==== Ae^(ikx - iwt)

====
solution using Eulers' rules
Acos(kx - wt) + iAsin (kx-wt)


are these answers right for above questions? or do the answers have to be more specific, i don't know I am new to all this.

ok when they ask to give a rule that determines all possible values of c what does that mean? this might seem dumb but I am not even sure what c is.


i registered for this forum specifically because I am having a lot of trouble in biophysical chem class, if anyone wants to help me it would be great.

 

[shrugBERT]

ooh and i can post any work leading up to the answers in the answer section but I refrained because I'm pretty sure my notation is horrible.