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zb23
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Why in order to derive the QM momentum operator we use the plane wave solution. Why later on in field theory and particle physics, the plane wave ansatz is so physically important?
That's the main basis for mathematical physics. Why represent force as a vector? Why is time a parameter in non-relativistic physics? Why have a spacetime manifold in relativity?zb23 said:I mean I can't be satisfied with the argument that it gives nice solutions.
Can you give some specfic references to arguments that you find lacking?zb23 said:some arguments for plane wave solutions, for me, lack some structure
You don't have to do it in that old-fashioned way.zb23 said:Why in order to derive the QM momentum operator we use the plane wave solution.
The plane wave solution is used for the momentum operator because it is a solution to the Schrödinger equation, which describes the behavior of quantum particles. This solution allows us to calculate the momentum of a particle in a quantum system with high accuracy.
The momentum operator plays a crucial role in quantum mechanics as it represents the observable quantity of momentum in a quantum system. It is used to describe the motion and behavior of particles at the microscopic level and is an essential tool in understanding the principles of quantum mechanics.
The plane wave solution is related to the uncertainty principle because it represents a state of definite momentum, which is a conjugate variable to position. This means that the more precisely we know the momentum of a particle, the less precisely we can know its position, and vice versa, as stated in the uncertainty principle.
Yes, the plane wave solution can be used for all types of particles, including both matter particles (such as electrons) and force-carrying particles (such as photons). This is because the Schrödinger equation and the momentum operator are applicable to all quantum systems, regardless of the type of particle.
While the plane wave solution is a highly accurate method for calculating momentum in quantum systems, it does have some limitations. It assumes that the particle is in an infinite, unbounded space and does not take into account any external forces acting on the particle. In situations where these assumptions do not hold, other methods may be more appropriate for calculating momentum.