The wave fuction for particle in a box

AI Thread Summary
The discussion revolves around solving the wave equation for a particle in an infinite potential well, specifically from x = -l/4 to x = 3l/4. The user initially struggles with boundary conditions and seeks tips for completing the problem. Suggestions include changing the variable to simplify the boundaries, which helps in normalizing the wave function. Ultimately, the user finds the solution, confirming the wave function as A sin(kx + kl/4) with A = √(2/a). This exchange highlights the importance of variable substitution and boundary condition understanding in quantum mechanics.
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Whwn i am doing exercise, i don't know how to solve the follow question by myself Although i hv the ans, i want to complete it by myself. Plz give me some tips only so that i can finish this question, please also tell me how do you know the question should be solved in this way.

The question requires me to solve the wave equation for a pacticle in a infinity potential well, from x=-l/4 to x= 3l/4
I let the wave equ be the form
Asinkx + B cos kx

and i got.
Asin(-kl/4) + B cos (-kl/4) = 0
and
Asin(3kl/4) + Bcos(-3kl/4) = 0

and than i can't do anymore
it is different from to x=0 to x= a case
What should i do? Any tips?
Is there any general solution for the wave fuction of the pacticle in a box from a point x to y?
 
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Change the variable to u=x+1/4.
 
thinks i am now trying to calculate
Could you please tell me why u know that the varible should be changed? Due to the experience? I am not good at physics but i love it should i do more exerience to develope this sence?
 
sorry
i don't get it
where should i change varible
do u mean that i should differinate the fuction?
I can't normalize it caz i don't know A abd B
 
clem meant "let u= x+ l/4" (it's a little difficult to distinguish between "l" ('ell') and "1" ('one') depending upon which font you use.) The only purpose of that is to change the boundaries from x= -l/4 and x= 3l/4 to u= 0 and u= 1 which makes the arithmetic slightly easier.
 
HallsofIvy said:
(it's a little difficult to distinguish between "l" ('ell') and "1" ('one') depending upon which font you use.)
Script ell ℓ is easier to read, one reason I use UTF.
 
Thank you guys. I got the answer. This skill is really useful for dealing with waves in the box.
The answer is : fuction = A sin (kx + kl(ell)/4) and A = root(2/a)
am i correct?:)
 
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