Category Archives: Schrödinger equation

Feynman’s Derivation of the Schrödinger Equation

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The traditional diffusion equation bore a family resemblance to the standard Schrödinger equation; the crucial difference lay in a single exponent where the quantum mechanical version was an imaginary factor, i. Lacking that i, diffusion was motion without inertia, motion without momentum. Individual molecules of perfume carry inertia, but their aggregate wafting through air, the sum of innumerable random collisions, does not. With the i, quantum mechanics could incorporate inertia, a particle’s memory of its past velocity. The imaginary factor in the exponent mingled velocity and time in the necessary way. In a sense, quantum mechanics was diffusion in imaginary time.

— page 175

— Genius: The Life and Science of Richard Feynman

— James Gleick

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2024.07.10 Wednesday ACHK

Trajectory

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It is not possible to derive Schrödinger’s equation from “anything we know”.

— R. P. Feynman

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The most confusing part in the Quantum Mechanics is [the concept of] Trajectory.

There exist[s] no fixed path for a particle to go from Point A to Point B. This is clearly visible from [the] Interference Experiment.

So, the approach here is to work with deductive reasoning. We eliminate the possible region/paths which [are] impossible to be followed.

To do this we assume that Energy Conservation Relation is valid for Quantum Mechanics too. So, those regions where particle[s] [violate] this law automatically [get] eliminated.

Then, we guess [the] State Function[s] for certain conditions i.e. how it should be in certain cases, then build an energy conservation equation with that. We will shortly demonstrate how Schrodinger itself reached the conclusion.

— Why can’t the Schrödinger equation be derived?

— Abhas Kumar Sinha

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2021.02.28 Sunday ACHK