Responsible party: Schrödinger's Dog, Devlin

The main points of today's lecture were:

• discussion and interpretation in quantum mechanics (i.e. <p>, <math>\Psi^*\Psi dx=P(x)dx</math>, etc…)
• Bohm's postulate and Yuichi's discussion on how Bohm's may have used classical ideas to come up with <math>\Psi^*\Psi dx=P(x)dx</math>
• Why we use <math>|\Psi|^2</math>, and not just <math>\Psi</math>, or some linear combination of <math>\Psi</math> for the probability

*normalization for t=0 and how the normalization works for time t * How partial derivatives and ordinary derivatives are used and the justification of the equation <math> \frac{d}{dt} \int_{-\infty}^{\infty}\Psi^*\Psi dx=\int_{-\infty}^{\infty}\frac{\partial}{\partial t}(\Psi^*\Psi)dx=0</math>

In the beginning of lecture, Yuichi discussed how <math> m\frac{d<x>}{dt}</math> is interpreted to be <p> and how we get this interpretation from the classical idea that p=mv. Yuichi then went on to discuss how <K> is found from the interpretation that <math> <K>=\frac{<p>^2}{2m}=-\frac{\hbar}{2m}(\frac{\partial}{\partial x})^2</math> and how this