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Proving Vector Identity Using Levi-Civita Symbol

Tuesday, June 28th, 2011

Roel N. Baybayon MSPhysics1 ————————————————————————————————– We are going to prove the following vector identity using Levi-Civita symbol: Solution: Let    ,     ,   ,   . Then, By definition: We have to let m=n so that, Levi-Civita symbol can be expressed in terms of Kronecker delta given by: Thus,    

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Vector Identity Formula #12 verified by using Levi-Civita

Monday, June 27th, 2011

Hi, guys! The following is my solution on verifying these two vector identity formulas. Show that (a) and (b) Solution: Let and (a) since and Thus, and (b) since and Therefore, About Me: I am Yusof-Den Jamasali, an MS Physics student of Mindanao State University – Iligan Institute of Technology. I like painting, and drawing. […]

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LOWEST-ORDER RELATIVISTIC ENERGY CORRECTION OF 1-D HARMONIC OSCILLATOR

Monday, March 22nd, 2010

Lotis R. Racines and Edwin B. Fabillar In quantum mechanics, relativistic correction to the energy levels of a system is used when it is introduced by a little disturbance we often recognized as [eq] \lambda [/eq]. Fine structure is an example of this where the splitting of spectral lines of atoms is due to its […]

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On the EPR paper “Can Quantum-Mechanical Description of Physical Reality be Considered Complete?”

Sunday, March 21st, 2010

LUTCHIE DYAN S. MENDOZA In the May 15, 1935 issue of Physical Review , Albert Einstein co-authored a paper with his two postdoctoral research associates at the Institute for Advanced Study, Boris Podolsky and Nathan Rosen. The paper, known as EPR, became a centerpiece in debates, challenging the validity of Quantum Theory. The paper features […]

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Commutation of Spin, Angular and Spin-Orbital Momentum

Saturday, March 20th, 2010

Marichu T. Miscala In quantum mechanics, the presence of spin-orbit coupling gives rise to the Hamiltonian that will no longer commute with [eq]\vec{L}[/eq], and [eq]\vec{S}[/eq], so the spin and orbital momenta are not separately conserved. In order to understand this concept better, a commutation problem for orbital angular momentum [eq]\vec{L}[/eq], spin [eq]\vec{S}[/eq], and spin-orbital momentum [eq]\vec{J}[/eq] is […]

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