Wave function?

Question

Why is a wave equation sometimes written as y = A*Cos (kx - wt) instead of A*Sin(kx - wt) ? What is the relationship?

Answer 1

A*sin(kx-wt) and A*cos(kx-wt) are equvalent except they are 90° out of phase. When you plot them, the sin function will be zero when (kx-wt) = 0, and the cos function will be 1 when (kx-wt)=0.

Answer 2

A wave function is a mathematical tool that quantum mechanics uses to describe any physical system. It is a function from a space that consists of the possible states of the system into the complex numbers. The laws of quantum mechanics (i.e. the Schrödinger equation) describe how the wave function evolves over time. The values of the wave function are probability amplitudes; complex numbers whose square gives the probability distribution that the system will be in any of the possible states. For example, in an atom with a single electron, such as hydrogen or ionized helium, the wave function of the electron provides a complete description of how the electrons behave. It can be decomposed into a series of atomic orbitals which form a basis for the possible wave functions. For atoms with more than one electron (or any system with multiple particles), the underlying space is the possible configurations of all the electrons and the wave function describes the probabilities of those configurations.

Answer 3

cos wave is a PI/2 translation of sin waves and vise versa...

Answer 4

They are identical except for the phase shift.

Answer 5

cos(Θ) = sin(Θ+π/2)

HTH

Doug