The Schrödinger equation is linear in time but does not exhibit time invariance, contrasting with other fundamental laws such as Maxwell's and Newton's equations. This lack of time invariance is attributed to the nature of the time reversal operator, which is antiunitary, requiring a complex conjugation of the wave function in addition to a sign change in time. In contrast, the Dirac equation, which employs first-order derivatives, maintains time invariance and respects relativistic principles.
PREREQUISITESPhysicists, quantum mechanics students, and researchers interested in the foundations of quantum theory and the relationship between time symmetry and relativistic equations.
And it does not respect any more the relativistic invariance.Avijeet said:The Schrödinger equation is linear in time. I was wondering if that means that is not invariant under time reversal. That would be a surprise because all other microscopic laws (Maxwell's equations, Newton's equations) are time invariant.