Varying mass in Schrodinger Equation

[hermitian]

hi,

today i learned that if the mass in Schrödinger equation is not a constant, then Schrödinger equation is not valid. Is there any reason why is it so?

Also, what is the different of the time dependent mass $$m(t)$$ and let say a time dependent angular frequency $$\omega(t)$$ in a harmonic oscillator. it seems that the latter is allowed but not the mass.

thank you!

 

[sokrates]

Are you talking about relativistically varying mass?

Then, you should use (or understand) the Dirac equation which incorporates the relativistic effects to the Schrödinger equation.

But if you are talking about non-relativistic particles where a series of changes in the transport medium is involved (say, an electron entering a dielectric from a metal, as in the case of Magnetic Tunnel Junctions, or SiO2 dielectric breakdown models where electrons in the silicon penetrate into the oxide due to extreme electric fields)
then you spatially vary the EFFECTIVE MASS, if such an approximation is appropriate.

These are the only two examples that I can think of "mass" varying in the Schrödinger equation