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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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Perturbation Theory: Quantum Oscillator Problem

Monday, April 20th, 2009

by ANCELIE C. ROSALES In quantum mechanics, the perturbation theory is a very important mathematical tool which is used to approximate physical quantities that describe complicated quantum systems based on our knowledge on the simpler ones. It tells us how to correct the solutions to the unperturbed or undisturbed problem to approximately account for the […]

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Properties of Quantum Oscillators 1

Friday, April 3rd, 2009

by SIMON JUDE BURGOS In this post we investigate the properties of a quantum oscillator by using an algebraic tool in quantum mechanics called ‘ladder operators’. Using the ladder operator it becomes easy to find the following properties for a quantum oscillator in a given energy level:  the average position and momentum and the square […]

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Properties of Hermitian Operators

Friday, March 13th, 2009

by BEBELYN A. ROSALES Linear operators in quantum mechanics may be represented by matrices. A type of linear operator of importance is the so called Hermitian operator.  An operator is Hermitian if each element is equal to its adjoint. Most quantum operators, for example the Hamiltonian of a system, belong to this type. Now linear […]

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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 […]

Posted in Linear Vector Space, Quantum Physics, Quantum Science Philippines | 24 Comments »