Saturday, January 21, 2006

GEOMETRIC INTERPRETATION OF SCHRÖDINGER'S FORMULA

If we try to take a Geometrical interpretation of Schrödinger's formula, we can see that in this formula there are two questions to solve, one, the minus sign in the formula, and two, the two terms of this, that seems to be rotations in different direction.

We have said that quaternions are very useful like rotation operators, and this, if we apply a quaternion to a vector and his conjugate complex, we have a rotation in one direction.

Thus

q v q* = (q)* v (q* )* = p* v p where p = q*


The identity is a rotation using p, that is the inverse rotation.

So, previous equation indicates us a rotation, and its inverse in negative direction, so we have two rotations in same direction, that is a rotation. This way, there are not efforts, and a free particle that we can use Schrödinger's equation is a redundancy.

If we want to use a formula with efforts, its necessary that it appears two term like this:





But, It exists any formula that has this terms? It's evident that the answer is YES.

We have the equation of continuity:



That has to be equal to zero, due to the condition of continuity.

Now, we can generalize the Schrödinger equation with efforts... next.

R. Aparicio.

Partial and not exactly extracted from "De Natura Visibilium Et Invisibilium". R. Aparicio. Ed. Elaleph.

1 Comments:

At 6:20 PM, Anonymous Anonymous said...

He seguido las formulaciones, y hasta ahora no encuentro ninguna contradicción con lo existente. Es extraña tu forma de verlo, pero parece creíble.

 

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