I’ve been doing research on quantum mechanics, but am having trouble breaking the barrier between fundamentals and mathematics. I have a good understanding of the principles and basic calculations, but don’t know how to use them.
I want to know if there is a formula, preferably an algebraic one, that allows me to plug in variables about a particle in order to calculate the amplitude that the particle will travel to a certain position.
I’ve looked at Schodinger’s equation, but don’t have a good understanding of it and don’t know what many of the inputs mean.
My main goal, which is somewhat flexible, is to simulate a photon going from place to place in position space.
At first, I would do photons as they are easier to do calculations with. I would be, so to speak, Laplace’s demon, and know everything about the system. This includes
- The position in two dimensions of the particle
- The momentum of the particle
- The mass of the particle
- The current place in time of the simulation
- Constants such as Planck’s constant, the speed of light, etc.
Although I could do this without the exact formulas, I would much rather have the accuracy that comes with using them. Also, the goal is to simulate a quantum system, so it makes the most sense to use quantum mechanical equations!
This may be an obvious question. This might not have an answer or be possible. I just want to know if there is an equation that allows me to satisfy the goals previously stated.
As I’ve said, I’m a relative beginner to the quantum world, so please bear with me. Thanks for any help.