@BvUBvU said:
The more I think about it, the less I feel qualifiedgreswd said:
A non-closed form solution would be really good too, hopefully there's oneBvU said:From the variety of approaches for different kinds of potential functions I estimate a zero probability for a (usable) general solution.
Would be something like a free lunch
I believe the TISE generally produces families of discrete solutions, so a general solution would be in terms of both V(r) and parameters like quantum numbers, with the number of quantum numbers depending on the shape of V(r).BvU said:
niceBvU said:
The Time-independent Schrödinger equation is a fundamental equation in quantum mechanics that describes the behavior of a quantum system over time. It is a partial differential equation that relates the wave function of a system to its energy and potential.
The general solution to the Time-independent Schrödinger equation is a mathematical expression that describes the wave function of a quantum system at any point in time. It is a combination of the eigenfunctions of the Hamiltonian operator, which represents the total energy of the system.
The Time-independent Schrödinger equation is used to calculate the energy levels and wave functions of a quantum system. It is also used to predict the probability of a particle being in a certain position or having a certain momentum.
The Time-independent Schrödinger equation assumes that the system is in a stationary state, meaning its properties do not change over time. It also assumes that the system is isolated and not affected by external forces.
The Time-independent Schrödinger equation is related to the uncertainty principle in that it allows us to calculate the probability of a particle being in a certain position or having a certain momentum. This probability is inherently uncertain, as described by the uncertainty principle.
