fish830617 said:Given
[x,p] = i * h-bar,
prove that
<p|X|p'> = [i * h-bar / (p' - p)] * δ(p - p').
I don't understand why commutator matters with this proof?
dextercioby said:This is nonsense. The commutator is defined for the H-space operators, the thing you got to prove is for their distributional extensions.
Momentum representation is a mathematical tool used in quantum mechanics to describe the state of a particle in terms of its momentum rather than its position. It is often used in conjunction with position representation to provide a more complete picture of a particle's state.
Momentum representation is important because it allows us to understand the behavior of particles at the quantum level. It is also a useful tool for solving certain problems in quantum mechanics, such as calculating the probability of a particle to have a certain momentum.
Momentum representation and position representation are two different mathematical representations of the same physical system. Momentum representation uses the momentum of a particle to describe its state, while position representation uses the position of a particle. They are related through a mathematical transformation known as a Fourier transform.
In classical mechanics, particles are described using their position and momentum in terms of classical variables, such as position and velocity. In momentum representation, particles are described using quantum variables, such as wave functions and operators, which take into account the probabilistic nature of quantum systems.
Yes, momentum representation can be used for all types of particles, including elementary particles such as electrons and protons, as well as larger particles like atoms and molecules. It is a fundamental tool in quantum mechanics and is applicable to all quantum systems.