- #1
martinhiggs
- 24
- 0
Homework Statement
a particle of mass m, confined to a one dimensional infinite potential of
0[tex]\leq[/tex]x[tex]\leq[/tex]1 V(x) = 0
elsewhere V(x) = [tex]\infty[/tex]
Homework Equations
Choose as a trial wavefunction
[tex]\Psi[/tex](x) = Nx[1 - [tex]\alpha[/tex]x + ([tex]\alpha[/tex] - 1)x[tex]^{2}[/tex]]
Verify that
N[tex]^{2}[/tex] = [tex]\frac{K}{16 - 11\alpha + 2\alpha^{2}}[/tex]
The Attempt at a Solution
1 = <[tex]\Psi[/tex]|[tex]\Psi[/tex]>
1 = [tex]\int^{1}_{0}[/tex]Nx[1 - [tex]\alpha[/tex]x + ([tex]\alpha[/tex] - 1)x[tex]^{2}[/tex]] Nx[1 - [tex]\alpha[/tex]x + ([tex]\alpha[/tex] - 1)x[tex]^{2}[/tex]] dx
1 = N[tex]^{2}[/tex] [tex]\int^{1}_{0}[/tex] x[tex]^{2}[/tex][1 - [tex]\alpha[/tex]x + ([tex]\alpha[/tex] - 1)x[tex]^{2}[/tex]][tex]^{2}[/tex]
Is this right so far?? I'm not sure how to carry on. Should I expand the brackets??