Vectors | Quantum Science Philippines

### Proving Vector Identity Involving the Unit Vector Using the Levi-Civita and the Kronecker Delta

Wednesday, June 29th, 2011

*author: Michelle R. Fudot   Prove: ___________________________________________________________ Proof: First, we define the following vectors as: ; ; and Now,  if we let i=k, then . Furthermore, Now, the derivative of orthonormal basis , that is, and the derivative of a coordinate X, . Also, , thus = = = = It is noted that . […]

### Verifying a vector identity using Levi-Civita

Monday, June 27th, 2011

VERIFYING A VECTOR IDENTITY USING LEVI-CIVITA Bianca Rae B. Sambo Hello physics enthusiast! I am BR, a graduate student in Physics in Mindanao State University – Iligan Institute of Technology. Hope my solution will be of use to you. Keep visiting this site!   The vector identity to be verified using Levi-Civita is, where we […]

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### Schwarz Inequality

Thursday, April 23rd, 2009

Schwarz Inequality, also known as Cauchy–Schwarz inequality, Cauchy inequality, or the Cauchy–Schwarz–Bunyakovsky inequality, is useful in many Mathematical fields such as Linear Algebra. This Inequality was formulated by Augustin Cauchy (1821), Viktor Yakovlevich Bunyakovsky (1859) and Hermann Amandus Schwarz (1888). The uncertainty principle of quantum mechanics, which relates the incompatibility of two operators, rests on […]

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### Sticky: Basics of Linear Vector Spaces

Sunday, January 18th, 2009

by CARIEL O. MONTALBAN In quantum mechanics, I have learned that the wavefunctions, , reside in Hilbert’s space.  What is Hilbert’s space? I guess to answer this question requires exploring the basic  properties of Hilbert’s space. Hilbert’s space is a linear vector space whose elements, entities or components obey certain rules or axioms.  This means […]