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Initially, we derive two dimensional equation for Schrödinger time independent equation. Then how it becomes three dimensional by just multiplying by delta. How?

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John Rennie
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Mast-p2
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  • @AccidentalFourierTransform We can derive it , its complicated – InquisitiveMind Dec 21 '16 at 16:53
  • I would be pretty sure AFT is pulling your leg a little :), but he is right, no q.m book can show you a derivation of the S.E., any more than a math book derives an axiom. So your sentence is an assumptions or misunderstanding on your part. –  Dec 21 '16 at 16:54
  • @catapillar No , not a rigorous derivation. But enough to give a basic idea to Mast-p2 – InquisitiveMind Dec 21 '16 at 16:56
  • I thought S.E. was derived from conservation of probability, the measurement axiom, and the correspondence principle? – Sean E. Lake Dec 21 '16 at 16:59
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    It's not clear what you mean by "two-dimensional" or "multiplying by delta" here. The "delta" is the Laplace operator and there isn't any two-dimensional equation in what you posted. – ACuriousMind Dec 21 '16 at 17:03
  • @InquisitiveMind I made a similar "derivation" here. However, these type of "derivations" are not actual derivations of that equation. Instead, you should think of it as being ways to show that that equation (postulate) is reasonable. S.E is a postulate of QM. It is supposed to coup with the observations and experimental data. – J. Manuel Dec 21 '16 at 18:07
  • You misunderstood it. The "inverted delta" there is the nabla operator (a "vector" with the form $\nabla =\frac{∂}{∂x},\frac{∂}{∂y},\frac{∂}{∂z}$). In one space dimension it just becomes $\frac{∂}{∂x}$. – J. Manuel Dec 21 '16 at 18:34
  • Laplace operator https://en.wikipedia.org/wiki/Laplace_operator –  Dec 21 '16 at 19:19

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You have completely misunderstood it.Initially, we derived three dimensional equation for Schrodinger time independent equation. The term

$$ {\nabla^2\Phi}$$ is actually the double differentiation of $\Phi$ in three coordinates x,y,z . It is the Laplacian Operator.It means double differentiate x by keeping y,z as constant and so on.

InquisitiveMind
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