Everybody knows that the orbital momentum is "quantized" and its z-projection has integer eigenvalues in units of . Too few, however, know that it is, in fact, a quasi-particle angular momentum which is integer-valued, not the particle one!
To see it, let us consider two spinless particles with masses m1 and m2 coupled with any central potential, say, with . The quasi-particle with the reduced mass describes the relative particle motion and depends on both particles in a two-particle compound system. It is its orbital momentum which is quantized in terms of integer numbers, namely, ranges from to .
The particle-1 and particle-2 orbital (angular) momenta and , calculated relative to the system center of inertia, are just certain, generally non-integer fractions of .
In particular, and are not obliged to have integer values! Why? Because they are simply non-integer functions of operator and are determined with its eigenvalues. For example, in the non-relativistic Positronium (where the particle masses are equal), if , the electron orbital momentum has the following values of projections: -1/2, 0, +1/2.
Surprise! And the same statement is valid for the positron projections in Positronium. "Half-integer" projections of a particle orbital momentum are thus possible and there is no kidding in it.
The particle orbital momenta in a bound system with respect to the system center of inertia are not momenta of independent, non-correlated subsystems. On the contrary, they are related and the rule of addition of independent angular momenta, usually taught in courses of Quantum Mechanics, is not applicable to them.
- PHYSICAL SCIENCES
- EARTH SCIENCES
- LIFE SCIENCES
- SOCIAL SCIENCES
Subscribe to the newsletter
Stay in touch with the scientific world!
Know Science And Want To Write?
- The Five Stages Of A Dying Theory
- Something is wrong in the Arctic
- Is The X(5568) A True Resonance ?
- Order Patterned With Chaos - How Climate Is Predicted For Decades - With Exact Forecasts Only For Days
- Neanderthals: Not So Dumb
- Should Pregnant Women Be Concerned About BPA?
- Anomaly! Book Presentation At CERN On November 29
- " Yo Robert, can you debunk this: http://www.express.co.uk/news/weird/740551/end-of-world-apocalypse..."
- "Oh okay maybe they got upset in the same way you did. You could try pointing them towards my Nibiru..."
- "So you can guarantee to me that this is not real yeah thats all i want for this not to be real..."
- "No you don't. It's not real, it's a hoax, any astronomer would just LOL at the idea. These are..."
- "Do I need to do any of that then Mr walker just want the truth are me and my children in any danger..."
- Don't Drive 'Gene Drives' Into a Ditch
- Public Citizen Wants You Dead- Not Bacteria
- Pfizer's Centrum Silver Multivitamins Contain Pesticide, Paint, and Glass
- Fly me to the Moon, but hold the altitude sickness
- What's in an Egg? Demystifying the Labels
- Paper Scandal at Science? Microbeads Lying In the Weeds. With A Stolen Computer.