And it does not respect any more the relativistic invariance.Avijeet said:The Schrodinger 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.
The time invariance of the Schrodinger equation refers to the property that the equation remains the same regardless of the time at which it is solved. In other words, the time at which the equation is solved does not affect the results or solutions.
Time invariance is important in quantum mechanics because it allows us to make predictions and calculations about a system at any given time. This property also ensures that the principles of quantum mechanics remain consistent and accurate.
The Schrodinger equation is a mathematical representation of the time evolution of a quantum system. It is time invariant because it remains unchanged when the time variable is replaced with a different value. This means that the equation gives the same results regardless of the time at which it is solved.
There are certain cases where the Schrodinger equation may not exhibit time invariance, such as when external forces or perturbations are acting on the system. In these situations, the equation may need to be modified to account for these factors.
The time invariance of the Schrodinger equation is closely related to the conservation of energy in quantum systems. Since the equation remains unchanged over time, it ensures that energy is conserved and that the system's total energy remains constant throughout its evolution.