- #1
George Keeling
Gold Member
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- TL;DR
- Don't understand reasoning in book.
I am reading Relativistic Quantum Mechanics Wave Equations, 3rd ed. - W. Greiner and I'm on section 1.3 looking at a solution ##\psi## to the Klein-Gordon equation in the nonrelativistic limit.
The solution is split up:
$$\psi=\phi\exp{\left[-\frac{i}{\hbar}m_0c^2t\right]}$$and we then show that in the nonrelativistic limit ##\phi## obeys the Schrödinger equation (or "the free Schrödinger equation for spinless particles"). So far so good. But then Grainer writes "As the type of particle which is described by a wave equation does not depend upon whether the particle is relativistic or nonrelativistic, we infer that the Klein-Gordon equation describes spin-zero particles".
If ##\psi## had obeyed the Schrödinger equation in the nonrelativistic limit, I would understand the inference but not ##\phi##. Can anybody enlighten me?
The solution is split up:
$$\psi=\phi\exp{\left[-\frac{i}{\hbar}m_0c^2t\right]}$$and we then show that in the nonrelativistic limit ##\phi## obeys the Schrödinger equation (or "the free Schrödinger equation for spinless particles"). So far so good. But then Grainer writes "As the type of particle which is described by a wave equation does not depend upon whether the particle is relativistic or nonrelativistic, we infer that the Klein-Gordon equation describes spin-zero particles".
If ##\psi## had obeyed the Schrödinger equation in the nonrelativistic limit, I would understand the inference but not ##\phi##. Can anybody enlighten me?