Wave function properties
Singly valuedThe wavefunction must be singly valued, this is due to the wavefunction not being able to have two different probabilities of being in the same location.
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ContinuousThe wavefunction must be continous as the differential should be well behaved, it cannot be infinite. This means that any spikes of peaks in the wavefunction cannot occur.
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FiniteThe wavefunction must be able to be defined over all space, this is only possible when the wavefunction does not equal infinity at any point.
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OrthogonalOrthogonality is where the overlap of wavefunctions produced are equal to zero. This is a highly limiting factor in the possibility of wavefunctions that are allowed. This isn't to say that all along the x axis the overlap produces 0 it is the total sum of the overlap that is equal to zero.
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