This is a simple question which I'm sure has a simple explanation. While mass of the particle is explicitly included in the Schroedinger Equation, the charge is not. Why isn't it? Is it included along with the potential energy or...?
Chronothread said:While mass of the particle is explicitly included in the Schroedinger Equation, the charge is not. Is it included along with the potential energy?
I have a question...what would this "more general formalism" look like, mathematically ?f95toli said:...Hence, Schroedinger equations that involve a "real mass" are just special cases of a more general formalism...
Chronothread said:This is a simple question which I'm sure has a simple explanation. While mass of the particle is explicitly included in the Schroedinger Equation, the charge is not. Why isn't it?
Mass and charge need not be present in the same equation! They are quantities of different origin. Mass is related to a spacetime symmetry called Poincare symmetry.
All type of Charges show up in the equations of physics as a result of making those equations invariant with respect to some internal symmetries . Some of these (local) internal symmetries give rise to interactions. The strength of such interaction is determined by the corresponding charge.
For example; if you want the electric charge to appear in Schrodinger equation, you need to make this equation invariant under the local U(1) transformation:
[tex]\Psi(x) \rightarrow \exp \left(i q \Lambda (x) \right) \Psi(x)[/tex]
The Schrödinger's equation is a fundamental equation in quantum mechanics that describes the time evolution of a quantum state. It is named after physicist Erwin Schrödinger, who first proposed it in 1926.
In Schrödinger's equation, charge refers to the electric charge of a particle. It is represented by the symbol q and is a fundamental property of matter that can affect its behavior in quantum systems.
Charge is important in Schrödinger's equation because it is one of the factors that determine the potential energy of a particle in a given quantum system. This potential energy affects the behavior of the particle and can determine its allowed energy states.
In Schrödinger's equation, charge is represented by the electric potential V, which is a function of the position of the particle. This potential energy affects the wave function, which is the solution to Schrödinger's equation and describes the probability of finding the particle at a particular position.
Yes, Schrödinger's equation can be used to describe charged particles such as electrons. However, it is important to note that the equation does not explicitly include the concept of charge, but rather it is incorporated through the potential energy term V. This means that Schrödinger's equation can be used to describe a wide range of quantum systems, not just those involving charged particles.