I tried to write the matrix form of the operator.Orodruin said:How would you usually find the eigenvalues of an operator?
And that looked like? What did you do after that?ZeroFuckHero said:
I tried to write the matrix form of the operator.
A 3D Hilbert space is a mathematical concept used to describe the set of all possible states of a physical system in three dimensions. It is a vector space that satisfies certain mathematical properties, such as being complete and having an inner product defined on it.
The energy eigenvalues in the 3D Hilbert space provide crucial information about the possible energy states of a physical system. This allows for a better understanding of the behavior and properties of the system, and can be used to make predictions and calculations.
The energy eigenvalues are found by solving the Schrödinger equation, which is a fundamental equation in quantum mechanics that describes the time evolution of a physical system. This equation takes into account the potential energy and kinetic energy of the system to determine the allowed energy states.
The energy eigenvalues can be affected by various factors, such as the shape of the potential energy function, the strength of the interaction between particles, and the presence of external forces. These factors can change the allowed energy states and alter the behavior of the system.
The energy eigenvalues can be experimentally determined by measuring the energy levels of a physical system and comparing them to the theoretical values predicted by solving the Schrödinger equation. This can be done through various techniques such as spectroscopy or particle scattering experiments.