- #1

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[tex]i\hbar\frac{d\psi}{dt}=-\frac{\hbar^{2}}{2m}D^{2}\psi+(V+NV_{0})\psi[/tex]

then my question is how could we solve it approximately..thanks...

- Thread starter eljose
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- #1

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[tex]i\hbar\frac{d\psi}{dt}=-\frac{\hbar^{2}}{2m}D^{2}\psi+(V+NV_{0})\psi[/tex]

then my question is how could we solve it approximately..thanks...

- #2

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Note that V0 probably depends on x, and therefore you need to manage the change of variables x² -> Nx² in the potential term too.

If V0 as a dependence like VO(x/xref), then xref² has simply to be replaced by N xref². Should be simple.

- #3

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thanks..i manage in a very similar way described by you:

first i divide all equation by N e=1/N tehn we would have:

[tex]ie\hbar\frac{d\psi}{dt}=-\frac{e\hbar^{2}}{2m}D^{2}\psi+(eV+V_{0})\psi[/tex]

after that i define the Hamiltonian [tex]H_{0}=-\frac{e\hbar^{2}}{2m}D^{2}\psi+V_{0}\psi [/tex] to solve this i use the WKB approach as e<<<1

then after that i treat V as a perturbation and solve it to first and second order....

But what is this good for?..let,s suppose we have a Lagrangian of the form L0+V with the potential then we could add a term NV0 in the Feynmann Path-integral, to obtain the K0 propagator we use the development of Taylor of S near its classical solution in the form:

[tex] S[\phi]=S[\phi_{c}]+(1/2)\delta^{2}S[\phi_{c}]\phi^{2}+.....[/tex]

then we evaluate this functional integral to calculte K0,for the rest we use perturbation theory to calculate the corrections to first and second order...

first i divide all equation by N e=1/N tehn we would have:

[tex]ie\hbar\frac{d\psi}{dt}=-\frac{e\hbar^{2}}{2m}D^{2}\psi+(eV+V_{0})\psi[/tex]

after that i define the Hamiltonian [tex]H_{0}=-\frac{e\hbar^{2}}{2m}D^{2}\psi+V_{0}\psi [/tex] to solve this i use the WKB approach as e<<<1

then after that i treat V as a perturbation and solve it to first and second order....

But what is this good for?..let,s suppose we have a Lagrangian of the form L0+V with the potential then we could add a term NV0 in the Feynmann Path-integral, to obtain the K0 propagator we use the development of Taylor of S near its classical solution in the form:

[tex] S[\phi]=S[\phi_{c}]+(1/2)\delta^{2}S[\phi_{c}]\phi^{2}+.....[/tex]

then we evaluate this functional integral to calculte K0,for the rest we use perturbation theory to calculate the corrections to first and second order...

Last edited:

- #4

Dr Transport

Science Advisor

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Solve for the [itex] NV_0 [/itex] and then use perturbation theory for the other potential.....

- #5

reilly

Science Advisor

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Regards,

Reilly Atkinson

Regards,

Reilly Atkinson

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