Is it possible to derive the Shrodinger's equation(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

i\hbar\partial_t \Psi(t,p) = \frac{|p|^2}{2m}\Psi(t,p)

[/tex]

in momentum representation directly from a path integral?

If I first fix two points [itex]x_1[/itex] and [itex]x_2[/itex] in spatial space, solve the action for a particle to propagate between these point in time [itex]\Delta t[/itex], and then take the limit [itex]\Delta t\to 0[/itex], the action approaches infinity.

If I instead fix two points [itex]p_1[/itex] and [itex]p_2[/itex] in the momentum space, solve the action for a particle to propagate between these points in time [itex]\Delta t[/itex], and then take the limit [itex]\Delta t\to 0[/itex], the action does not approach infinity, but instead zero. So it looks like stuff goes somehow differently here.

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# Path integral in momentum representation

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