# The wave fuction for particle in a box

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In summary, the question asks for a wave function for a particle in a potential well, from x=-l/4 to x= 3l/4. The function is given by Asinkx + B cos kx, and the solutions can be found using sin(-kl/4) + B cos (-kl/4) = 0 and sin(3kl/4) + Bcos(-3kl/4) = 0. Once the solutions are found, it is impossible to continue solving because the boundaries for x=0 to x= a case have been changed.f

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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?

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.

(it's a little difficult to distinguish between "l" ('ell') and "1" ('one') depending upon which font you use.)
Script ell 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