Word Gems: Quantum Mechanics: What is the Schrodinger Equation?

In the Copenhagen Interpretation, the Measurement Problem arises from the Schrodinger Equation. When the Schrodinger Equation is solved, the answer is not a number but another equation called the “wave function.” The wave function describes an evolving wave. At no point does the wave function describe transformation of the wave to a particle. Yet, we know, that upon measurement, we will find not a wave, but a particle.

The wave function tells us the probability of where we will detect the particle. Though the wave function omits description of the transformation from wave to particle, it is accurate in predicting the collection of resulting positions in which particles are found in the course of many runs of the experiment.

Mathematically, the moment of measurement is the moment in which the wave function “collapses.” The mathematical description of wave function collapse is that the probability of finding the particle (in this case a photon) where it was detected goes to 100% and the probabilities of finding it in all other positions fall to zero.

from https://sciencing.com/schrodingers-equation-explained-how-to-use-it-13722578.html

The Schrodinger equation is the most fundamental equation in quantum mechanics, and learning how to use it and what it means is essential for any budding physicist. The equation is named after Erwin Schrödinger, who won the Nobel Prize along with Paul Dirac in 1933 for their contributions to quantum physics.

Schrodinger's equation describes the wave function of a quantum mechanical system, which gives probabilistic information about the location of a particle and other observable quantities such as its momentum. The most important thing you’ll realize about quantum mechanics after learning about the equation is that the laws in the quantum realm are very different from those of classical mechanics.

The Wave Function

The wave function is one of the most important concepts in quantum mechanics, because every particle is represented by a wave function. It is typically given the Greek letter psi (?Ψ?), and it depends on position and time. When you have an expression for the wave function of a particle, it tells you everything that can be known about the physical system, and different values for observable quantities can be obtained by applying an operator to it.