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What is a wave? What does this motion really mean, in physical terms? What does it mean for energy to travel in such a manner? When you have something that is traveling as a wave, and you characterize it with a wave function, are you looking at one slice of the motion because the energy is actually traveling with this wave characteristic in 360 degrees? Is this wave pattern how it behaves in every direction, and the only thing that is unique to a given energy is wavelength and amplitude? Why do wavelength and amplitude change and what affects this change? What changes amplitude and what changes wavelength?

Why do sine and cosine functions describe waves? Why do they describe every kind of wave motion possible? How do they describe waves? How does the sine or cosine function work such that it captures the behavior of something that oscillates and, what causes things to oscillate in this manner?

From all of this, if you have Acos( ((2pi)x/lambda) - ((2pi)frequency*time)), what do each of these components mean? Is the component involving frequency a decay of the oscillation? Do you have to even consider decay in quantum? Is this a nonsensical question? If you do consider a decay, is the decay representative of factors which change wave functions of particles as they change energy states?

Is the wave function always of the form Acos(((2pi)x/lambda) - ((2pi)frequency*time))? Do you ever use sine instead of cosine?

When you say that the schrodinger wave equation is a function of position and time but, you can hold one or the other constant to take the equation to be a function of either position or time, what does that mean? The text represents a cosine wave if position is on the x axis and psi, the wave equation, is on the y axis, while time is constant, but, it shows only arrows propagating along the y axis, marked to indicate psi, the wave equation, when position is held constant and time is varied. (Quantum Mechanics, An Accessible Introduction. Robert Scherrer) I don't understand what this means, how it works that way, or why it works.

If anyone can offer me a dumbed-down explanation of the wave equation, or wave equations in general, I would really appreciate it.

Sincere thanks.

M.