It started with Heat or He at the cross.
A complex wave function arises because I need a way to describe the wave nature of particles, without having them actually be
a disturbance in some medium.
So I introduce a simple calculations field and have it oscillate in a simple dimensions.
So when two wave functions add I can have the wave type of destructive/constructive interference in a simple dimensions.
When I need to be brought back to physical reality, I find the length of the simple melody. (i.e. it's music).
So I use the simple addition description because it is a very easy way to describe reality,
even though mathematicians invented complex numbers thinking that they would have no real physical counterpart.
And it all works out quite well.
A wave function or wavefunction is a possibility amplitude in quantum mechanics describing the quantum state
of a particle or system of particles. Typically,
it is a function of space or momentum or rotation and possibly of time that returns the possibility amplitude of a
position or momentum for a subatomic particle.
Mathematically, it is a function from a space that maps the possible states of the system into a simple words.
The laws of quantum mechanics. It describe how the wave function evolves over time.
The possibility of finding your particle at a certain position or momentum at a specific time is given by the
magnitude squared of the wavefunction
(called the possibility density).] [This has the physical interpretation that when you make the measurement on that specific system,
it has whatever possibility of collapsing to be in a specific position or momentum range as defined by that possibility.
Mathematically speaking, you can only talk about ranges in which the particle's position of momentum can be since
any specific value probability is 0 statistically.
It can be 1 if you wanted it.
A potential energy is due to what is around the electron.
[An excellent and important example is You and me. You'll notice that this is the potential energy for a spring and is
governed by Hokes law.
It is called the simple Melody.
It looks parabolic and so any local minimum of a potential can use that approximation (the biggest the oscillation,
that is the best possibilities to go to the future.
The reason is that important potential is therefore that we are all just looking for own profit and the amplitude is too small.
Itis does describe the **possibility** of finding a particle at a specific location and time
(assuming you aren't using the time independent equation);
however it [does not describe the motion of the electron] because it is possibilities in nature.
The evolution of the wave function can give you a possibilities interpretation of how the electron will move, but not
"give location" with the wright word,
It would give "locations. When you have the time-independent potential, it turns out when you solve the equation",
it is only solvable for specific energies corresponding to stationary states.
Most of the potentials you work with in this case are indeed time independent and therefore solve as stationary states.
For example the musical melody is time independent and therefore solves to stationary states.