Normalization constant of lineer combination of two waves?

[sylar88]

Homework Statement

$$\psi$$=B( sin px/L + sin 2px/L )

Homework Equations

lineer combination of two waves n=1 and n=2 states particle in a box wide L

The Attempt at a Solution

I have no idea how to calculate lineer combination of two waves normalization. How do I get B normalization constant??

 

[tiny-tim]

welcome to pf!

hi sylar88! welcome to pf!

(have a psi: ψ )

learn your trigonometric identities …

sinA + sin B = … ? ​

 

[sylar88]

but when ı take the form of 2 [sin (3px/2L). cos (px/2L)] how do ı calculate its integral. Can ı use mathematical methods then integrate it and it will equal to 1. So ı find t normalization constant B ? Take boundries of integral 0 to L ?

 

[sylar88]

pls help me ı need answer just say me my prediction is true :/

 

[tiny-tim]

hi sylar88!

but when ı take the form of 2 [sin (3px/2L). cos (px/2L)] how do ı calculate its integral.

try integrating by parts twice, then a bit of algebra

 

[sylar88]

hi sylar88!


try integrating by parts twice, then a bit of algebra

What about boundries?? 0 to L can ı take ? what about n=1 n =2 Where do ı use them

 

[tiny-tim]

yup … 0 to L (or x)

(what's n ? )

 

[sylar88]

yup … 0 to L (or x)

(what's n ? )

Question says that solve the equiaton combination of wave functions for the n= 1 and n=2 states in a particle of box wide L.

 

[tiny-tim]

oh, right!

but you've already used them, in your original equation …

you're now solving it​

 

[sylar88]

oh, right!

but you've already used them, in your original equation …

you're now solving it​

Its logical thank you for your interest and help. I will come for new questions )