Why is the Schrödinger equation not Lorentz invariant?

The Schrödinger equation of one body quantum mechanics is clearly not manifestly Lorentz invariant, not if the wavefunction is treated as a scalar function. This is due to the occurrence of one time derivative but two space derivatives in the equation.

Why is the Schrödinger equation that we have set up in this class called the non-relativistic equation?

The Schrödinger equation is non-relativistic by construction. It follows from the nonrelativistic classical energy expression by applying De Broglie’s idea to replace (E,→p) by −iℏ(∂t,→∇). There is nothing relativistic about this. In fact this is not even really a full theory.

Is the Schrödinger equation Relativistically correct?

The Schrödinger equation is a non-relativistic approximation to the Klein-Gordon equation. The properties (momentum, energy.) described by solutions of Schrödinger equation should depend in the proper way of the Galilei reference frame. In reality they don’t.

What is H in Schrodinger wave equation?

The hydrogen atom, consisting of an electron and a proton, is a two-particle system, and the internal motion of two particles around their center of mass is equivalent to the motion of a single particle with a reduced mass.

Why Schrodinger equation is not valid for relativistic particle?

Why is the Schrodinger wave equation not for relativistic particles? Because it is based on Newtonian physics rather than relativistic. It’s just classic kinetic energy + potential. There is no mass energy, no relativistic corrections etc.

Is wave function Lorentz invariant?

These wave functions are not Lorentz-invariant, because the shape of the wave function changes as it is Lorentz-boosted. However, the wave function is Lorentz-covariant under Lorentz transformations.

What is non-relativistic formula?

This is clearly a statement of the non-relativistic energy-momentum relation, E=12mv2, since a time derivative on a plane wave brings down a factor energy.