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eljose

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SE equation in (1d) [tex]a\frac{d^{2}\phi}{dx^{2}}+V(x)\phi=E_{n}\phi [/tex] (1)

WKB approach [tex]\phi=exp(iW/\hbar)[/tex] (2)

[tex]W=[2m(E_{n}-V)]^{1/2}[/tex]

then from (2) we can obtain the potential and introduce it in (1) to get a differential NOn-linear equation...

[tex]a\frac{d^{2}\phi}{dx^{2}}+(b/phi)^{2}(\frac{d\phi}{dx})^{2}+c\phi=0 [/tex] we could use this to prove that always the eigenfunction of the Hamiltonian [tex]\phi[/tex] will exist...

WKB approach [tex]\phi=exp(iW/\hbar)[/tex] (2)

[tex]W=[2m(E_{n}-V)]^{1/2}[/tex]

then from (2) we can obtain the potential and introduce it in (1) to get a differential NOn-linear equation...

[tex]a\frac{d^{2}\phi}{dx^{2}}+(b/phi)^{2}(\frac{d\phi}{dx})^{2}+c\phi=0 [/tex] we could use this to prove that always the eigenfunction of the Hamiltonian [tex]\phi[/tex] will exist...

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