Eigenvalues And Eigenvectors | Quantum Science Philippines

### Generalized Legendre differential equation

Friday, May 24th, 2019

Vanessa V. Destura, MSU-IIT Starting with an eigenvalue equation, where Also, we set So, substituting the given values, we find Now, by separation of variables, the equation yields to Let . So, Note that So, Thus, the associated Legendre differential equation is Since the solutions are symmetric in , assume . So, Using Frobenius method […]

### Derivation of the ladder operators for the Orbital Angular Momentum, L

Wednesday, May 22nd, 2019

Vanessa V. Destura, MSU-IIT Let be an eigenvector of and with eigenvalues and respectively. Now, we take the square of the norm of the eigenvalue equations for and For : For :   where Note that We expand the left-hand side of the equations obtained for (equation ) and (equation ) and substitute equations and […]

### Eigenvectors and Eigenvalues of a Perturbed Quantum System

Wednesday, June 24th, 2009

by  HENRILEN A. CUBIO Finding the eigenvectors and eigenvalues of the state of a quantum system is one of the most important concepts in quantum mechanics. And it is here where many students get confused. In order to learn this by heart, one has to do several exercises.  There are many ways that can be […]

### Simultaneous Diagonalization of Hermitian Matrices

Friday, May 8th, 2009

by MARYJANE D. MADULARA In an earlier post about the properties of Hermitian operators, it was noted that quantum operators of physical significance are Hermitian by type. Here we discuss more fully about Hermitian matrices. A n x n matrix is Hermitian if it is equal to its corresponding adjoint matrix. Now, for each Hermitian […]

### 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 […]