Time invariance of Schrodinger equation

[Avijeet]

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.
Can you please clear this doubt?

 

[Jacques_L]

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.

And it does not respect any more the relativistic invariance.
Only the Dirac equation does. It only uses first order derivatives.

 

[vuellesse]

Actually it is time invariant, since the time reversal operator is not unitary but antiunitary, so you have to complex-conjugate the wave function besides changing the sign of the time.
Of course it doesn't respect relativistic invariance.