Alpha in the schrodinger's equation for the harmonic oscillator

[asdf1]

why for that equation does alpha= 2E/(hf)?

 

[Galileo]

Since you haven't mentioned what alpha is supposed to represent, how are we to supposed to answer that question? I can't read minds you know. Alpha is not an agreed upon universal variable.
To me it sounds like a definition. There to simplify notation.
It is equal to the ration of the energy to the ground state energy.

 

[asdf1]

sorry for being unclear~
psi`` + (2m/H^2)(E-0.5kx^2)psi=0
my textbook says that to simply that equation, it makes the subsitution
alpha= 2E/(hf) so that
psi``+(alpha-y^2)=0
but i think that it should make the subsitution y= (2m/H^2)E

 

[jtbell]

but i think that it should make the subsitution y= (2m/H^2)E

So go ahead and try it and see if it helps better than the other substitution! It's certainly possible that it might work. There's usually more than one way to skin a cat (or solve an equation), after all.

 

[asdf1]

you're right~ :)
just curious why the book made that substituition, though~