- #1
BenR-999
- 5
- 0
Have to find the probability of measureing the ground-state energy of a particle.
-in infinite potential well 0<x< a
has wave-function \psi (x,0) = Ax(a-x)
where a is the (known) length of the well, and the norm. const. A has already been found.
The eigenvalues of the hamiltonian in this potential are;
\phi_n = \sqrt{\frac{2}{a}} \sin(\frac{n \pi x}{a}})
I think that to do this i should take
\left| \langle \psi | \phi_n \rangle \right|^2
for n=1.
which becomes
\left[ \int^a_0 \psi \phi_1 dx \right] ^2 (as all are real-valued)
I'm not sure if this is correct..it just seems a little to simple.
(with A=\frac{ \sqrt{30} }{a^{5/2} }
i got 60/ \pi ^2 which is obviously incorrect..as it is greater than 1.
But, if the method is correct and i have just made algebra error?
Thanks
-in infinite potential well 0<x< a
has wave-function \psi (x,0) = Ax(a-x)
where a is the (known) length of the well, and the norm. const. A has already been found.
The eigenvalues of the hamiltonian in this potential are;
\phi_n = \sqrt{\frac{2}{a}} \sin(\frac{n \pi x}{a}})
I think that to do this i should take
\left| \langle \psi | \phi_n \rangle \right|^2
for n=1.
which becomes
\left[ \int^a_0 \psi \phi_1 dx \right] ^2 (as all are real-valued)
I'm not sure if this is correct..it just seems a little to simple.
(with A=\frac{ \sqrt{30} }{a^{5/2} }
i got 60/ \pi ^2 which is obviously incorrect..as it is greater than 1.
But, if the method is correct and i have just made algebra error?
Thanks