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.
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 dont know im 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 im not even sure what c is.
i registered for this forum specifically because im having alot of trouble in biophysical chem class, if anyone wants to help me it would be great.