The most important concept to understand when working with quantum mechanics, is that nothing is precise. SInce everything is in a state of superimposed, the following concepts would be metaphysics. There is no true understanding to quantum mechanics, we are only working with probabilities and impossibilities.
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'The Theory of Quantum Mechanics and Momentum'
The statistical interpretation to this, is the foundation for all theories. It is nothing but a sound interpretation using a minimum of assumptions. There is an inability to find the exact point, as quantum mechanics, as stated before, is an incomplete theory in itself. The probability density for electrons, the particle itself, the time, and even the region of probability, cannot be predetermined. Meaning, the probability of the wave function is not one that can be pinpointed. Although mathematical equations can be used to supposedly determine the position, momentum, energy and velocity, that would be considered inaccurate. Seeing as nothing can be predetermined or checked, the answer is also nothing. There are some things in which we fail to understand.
However, the solution of the statistical interpretation must be normalized nonetheless. This is simply put, as how probabilities add to one, it is to get rid of infinitives, which can prove tricky to work with. However at times, the integral of the equation is infinite, meaning no multiplicative factor is going to make it to one. Non-normalizable solutions cannot represent particles, and so they are therefore rejected.
The equations for momentum follow a very similar pattern to normalization. Although there are different kinds of momentum in regards to quantum mechanics, we are only trying to find the average of measurements performed on all particles in that state. Most importantly, the particles must all be returned to its original state, or to measure the ensemble of particles. Although the X value, is the expected velocity, we are still finding an impossibility. The meaning of velocity itself in quantum physics is unclear. Meaning, there is no determined position, therefore you cannot find the velocity.
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To move forward to different types of momentum, there is the spin angular momentum. All elementary particles have a characteristic spin with their own measurements. The orbital angular momentum is the predicted position, and the predicted momentum, to equal the cross product. So with this in mind, both the spin angular momentum and the orbital angular momentum, are put together for the total angular momentum. Both the orbital angular momentum and the spin angular momentum are actually equal to the entire universe. The universe is the only remaining constant in this equation, and is still a value left undetermined.
