How I hate thee. Let me count the ways:
I do not care where thou havest poles.
Calculate your own contour integrals; i havn’t the inclination nor the time to learn.
Your Laurent series are laughable; your principle part despicable.
Your numbers are but a figment of imagination from some demented mathematician’s mind.
(sqrt(cos(x))*cos(200 x)+sqrt(abs(x))-0.7)*(4-x*x)^0.01, sqrt(9-x^2), -sqrt(9-x^2) from -4.5 to 4.5
The time dependent Schrödinger equation gives the first time derivative of the quantum state. That is, it explicitly and uniquely predicts the development of the wave function with time.
5 hours.
Leggo.
Noether’s theorem was proposed by Emmy Noether in 1918. It relates symmetries of a system to conservation laws. Roughly speaking, Noether’s theorem says that if there are ways we can transform a system continuously in some way without changing it, there must be some corresponding quantity that is conserved with time.
Consider doing an experiment somewhere in empty space. The outcome of the experiment will be the same no matter where you do it; this corresponds to a conservation in linear momentum. If you can perform the same actions no matter your direction of orientation in space, you are exhibiting conservation of angular momentum. If you can perform the same experiment at any time, your system shows conservation of energy.
If you know a bit of classical mechanics (Lagrangians and such), you can see where Noether’s theorem comes from (read moar here). Basically if you write a lagrangian for something that is independent of a certain coordinate (position, for example), the time rate change of a corresponding quantity (momentum for example) will be zero: hence, conservation.
This idea of symmetries corresponding to conservation laws has been applied to fields: for example, you can use Noether’s theorem to prove a form of charge conservation via symmetric transformations of the electric field.
