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?
- Dopamine Receptor Agonist Drugs Linked To Gambling And Hypersexuality
- New Tractor Beam Can Repel And Attract
- What's Hiding Under The Clouds Of Venus - Heavy Metal Frost?
- Amenhotep III: Ancient Egyptian Mummies Didn't Have Spinal Arthritis
- #GAMERGATE Style Harassment Does Not Happen in the Male Dominated Sciences
- Get A Heart On: Viagra Is Good Outside The Bedroom Too
- Psychiatry Should Switch From Symptom-based Prescriptions To Target-based
- "I'll not argue that humanity made God in their image, because we sought to explain something we..."
- "I think we all are atheist, agnostics, and believers throughout our life time. I also, think some..."
- "Author-- Was it necessary to add the pejorative comment-- Even 2,000 years ago people made fun..."
- "The scenario mentioned above (Poor person shows up at emergency room with a fever... No health..."
- "Actually, I used to believe. It was what I was taught as a child and I was raised a Christian...."
- Mutagenesis: One way Europeans wish it was 1936 again
- Closer examination of risk factors for Latinos underscores cultural diversity
- Saving bees requires less pesticides, changing farming
- Could GM plants replace airport security scanners?
- In a battle of brains, chimpanzees match human toddlers
- ‘Urban farmers’ behind GMO labeling initiatives
- Measuring on ice: Researchers create 'smart' ice skating blade
- Paralyzed man recovers some function following transplantation of OECs and nerve bridge
- Exposure to traffic pollution during pregnancy can damage future child's lungs
- Non-smokers exposed to 3 times above safe levels of particles when living with smokers
- The Lancet: Three people infected with Ebola predicted to fly from West Africa every month if no exit screening takes place