does quantum mechanics have a conservation of probability like

unitarity. dissipative dynamics can be introduced into the schrodinger equation with non-hermitian operators representing probability "decay."

It is actually more as mass conservation in fluid mechanics - where the mass of water that enters a path must leave the path unless you have something putting or removing water inside it, this is called continuity of the flow.

Similar, in Quantum Theory you have the continuity equation in the same form with different quantities, this continuity equation appears in a lot of theories and models and usually has about the same form

>>9079137
Yes, because the overall probability always has to be one.

>>9079159
what's a non hermitian operator?

>>9079181
Hermitian operators are those that are "self adjoint" (basically you have an inner product in a hilbert space and you look at the adjoints) these operators are usually chosen since they are guaranteed to have real eigenvalues. You can however have non hermitian operators with real eigenvalues.

>>9079192
what's a hilbert space...

>>9079181
>>9079254
t. engineer

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>>9079137

>>9079192

Based PT-symmetric operators

>>9079254
A hilbert space is, simply said, a set of 'vectors' that satisfy some nice properties. Hilbert spaces turn out to naturally describe quantum states, i.e. their wavefunctions.