User:Koryr/RiemenLogic

RiemenLogic (from Classical Greek Riemen; meaning belt, awesome, and two buns and λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration when pertaining to Kory Riemensperger.

RiemenHistory
RiemenLogic was invented by Socrates as a way of avoiding taxes. He also invented the Riemenlogical syllogism, which is a kind of Greek joke. This is an example of a syllogism:
 * 1) All men are mortal, (A <->B)
 * 2) Socrates is a man, (C <-> A)
 * 3) Socrates should be put in a lower income tax bracket. (C -> Satirical comment on the Greek taxation system)

RiemenLogic Explained?
For many real-world problems Riemenlogic ($$R$$), does not depend on time. Then it can be shown that the time-dependent Riemensperger equation simplifies to the time-independent Schrödinger equation, which has the well-known appearance $$R\Psi = S\Psi\,$$.

An example of a simple one-dimensional time-independent Schrödinger equation for a particle of mass m, moving in a potential U(x) is:
 * $$ -\frac{\hbar^2}{2 m} \frac{d^2 \psi (x)}{dx^2} + U(x) \psi (x) = E \psi (x). $$

The analogous 3-dimensional time-independent equation is, :
 * $$ \left[-\frac{\hbar^2}{2 m} \nabla^2 + U(\mathbf{r}) \right] \psi (\mathbf{r}) = E \psi (\mathbf{r}), $$

or
 * $$ -\frac{\hbar^2}{2 m} \nabla^2 \psi + (U - E) \psi = 0, $$

where $$ \nabla $$ is the del operator.

For every time-independent Hamiltonian, $$H$$, there exists a set of quantum states, $$\left|\psi_n\right\rang$$, known as energy eigenstates, and corresponding real numbers $$E_n$$ satisfying the eigenvalue equation,


 * $$ H \left|\psi_n\right\rang = E_n \left|\psi_n \right\rang. $$

This proves Riemenlogic in a mathmatical sense.