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The '''Schrodinger equation''' is a linear [[differential equation]] used in various fields of [[physics]] to describe the time evolution of quantum states.  It is a fundamental aspect of [[quantum mechanics]].  The equation is named for its discoverer, [[Erwin Schrodinger]].

The '''Schrodinger equation''' is a linear [[differential equation]] used in various fields of [[physics]] to describe the time evolution of quantum states.  It is the fundamental equation of [[quantum mechanics|non-relativistic quantum meachincs]].  The equation is named after its discoverer, [[Erwin Schrodinger]].

==Mathematical forms==

==Mathematical forms==

===General time-dependent form===

===General time-dependent form===

The Schrodinger equation may generally be written

The Schrodinger equation may generally be written

===Interpretation of the Wavefunction===

===Interpretation of the Wavefunction===

The wavefunction is related to the probability of observing a particle at that location in space. More specifically, where the wavefunction has a greater value of <math>|\Psi|^2</math> at one location, a, compared to another, b, then the particle is more likely to be observed at a than b.

The wavefunction is related to the probability of observing a particle at that location in space. More specifically, where the wavefunction has a greater value of <math>|\Psi|^2</math> at one location, a, compared to another, b, then the particle is more likely to be observed at a than b.

====Normalisation====

====Normalisation====

Wavefunctions are said to be "normalisable" if the following integral exists:

Wavefunctions are said to be "normalisable" if the following integral exists:

===Derivation===

===Derivation===

The particle cannot exits outside the box where the potential is infinite. Hence the wavefunction, <math>\psi</math>, here must be zero outside the box. Now let us consider inside the box. The Schrodinger equation inside the potential well becomes:

The particle cannot exits outside the box where the potential is infinite. Hence the wavefunction, <math>\psi</math>, here must be zero outside the box. Now let us consider inside the box. The Schrodinger equation inside the potential well becomes:

where <math>\omega</math> is as above.

where <math>\omega</math> is as above.

==See Also==

==See Also==