Ciro Santilli @cirosantilli 37

The Schrödinger equation Hamiltonian has to be a Hermitian so we will have only positive energies I think: quantumcomputing.stackexchange.com/questions/12113/why-does-a-hamiltonian-have-to-be-hermitian

Because there is value in tutorials written by beginners:

TODO: use the results from the quantum harmonic oscillator solution to precisely illustrate the discussion at Schrödinger picture with a concrete example.

Contains the full state of the quantum system.

This is in contrast to classical mechanics where e.g. the state of mechanical system is given by two real functions: position and speed.

The wave equation in position representation on the other hand encodes speed in "how fast does the complex phase spin around", and direction in "does it spin clockwise or counterclockwise", as described well at: Video "Visualization of Quantum Physics (Quantum Mechanics) by udiprod (2017)". Then once you understand that, it is more compact to just view those graphs with the phase color coded as in Video "Simulation of the time-dependent Schrodinger equation (JavaScript Animation) by Coding Physics (2019)".

The photoelectric effect paper.

Forms a normal subgroup of the general linear group.

Schrödinger equation for a one dimensional particle with $V=0$. The first step is to calculate the time-independent Schrödinger equation for a free one dimensional particle

Then, for each energy $E$, from the discussion at Section "Solving the Schrodinger equation with the time-independent Schrödinger equation", the solution is:Therefore, we see that the solution is made up of infinitely many plane wave functions.

Mentioned at: en.wikipedia.org/wiki/Phase_transition#Modern_classifications

The more familiar transitions we are familiar with like liquid water into solid water happen at constant temperature.

However, other types of phase transitions we are less familiar in our daily lives happen across a continuum of such "state variables", notably: