BASIC ELECTRICAL ENGINEERING

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QUANTUM PHYSICS

Meson energy levels in a two step potential

Eigenvalues of a two step potential

Ground state energy of regularized coulombic one dimensional potential

Tunneling for the centrifugal barrier

Resonant Tunneling Diode

Transmission coefficient for a double potential barrier

Transmission coefficient for a potential barrier

Reflection by a step potential barrier (numerical approach)

Linear Potential in the Dirac equation (under construction)

Numerical solution to the Dirac equation

Scalar potential in the Klein-Gordon equation

Quantum Semi Oscillator

Quark confining potential in the Klein-Gordon equation (Part 1)

Bosonic Relativistic Harmonic Oscillator - Part 2

Bosonic Relativistic Harmonic Oscillator - Part 1

The Spherical Harmonic Oscillator

Pionic p - states in 207 Pb

Pionic s- states in 207 Pb

Radiation Reaction Force

Solution of the Schrodinger Equation with Potential ?A x exp(-alfa x^2)

Solution of the Schrodinger Equation with Cubic Potential

Gaussian Wave Packet

Time Dependent Quantum Mechanical Wave Function (Part2)

Time Dependent Quantum Mechanical Wave Function (Part 1)

Klein Gordon equation: an exact numerical solution (Part 2)

Klein Gordon equation: an exact numerical solution (Part 1)

LCAO Method: H2+ Molecule

One dimensional hydrogen molecule (Part 3)

Integrating the half delta function proper value problem

One dimensional hydrogen molecule ( Part 2)

One dimensional hydrogen molecule ( Part 1)

Lithium with Vee delta function potentials

Free Particle Propagator-Numerical treatment

Propagator for the particle in the box (Part - 2)

Propagator for the particle in the box (Part - 1)

One dimensional model for helium - Part 3

One dimensional model for helium - Part 2

One dimensional model for helium

Evaluation of the Electrostatic Potential of Electrons Using Poisson?s Equation

Time independent perturbation theory (Part 3)

Time independent perturbation theory (Part 2)

Time independent perturbation theory (Part 1)

Quantum Harmonic Oscillator With a Delta Function Perturbation

Correlated Ground State Energy of Helium

Correlated variation function for the helium atom

Helium variation calculation using Gaussian-Legendre Quadrature Integration

Helium variation calculation in six dimensional configuration space

Harmonic Oscillator Variational Calculation by Monte Carlo Method

The Logarithmic Potential (Part 2)

Numerical solutions of a hydrogenic atom in d-dimensions

The Logarithmic potential eigenvalues

The H2+ molecule-ion -Version 2

Beryllium one parameter variational calculation

Two Dimensional Quantum Hydrogen Atom

Coulombic (J) and Exchange (G) terms using scaled hydrogenic wave functions

Eigenvalues of the modified one dimensional electric dipole

CARBON - ONE PARAMETER VARIATIONAL CALCULATION

NEON ONE PARAMETER VARIATIONAL CALCULATION

Electron repulsion ?Vee- one parameter approximations

Plot of exchange energy term K1s2s

Approximation to the exchange energy term K1s2s

Total energy of lithium in the Hartree approximation

Total energy of lithium with a single variational parameter

Ground state of the modified -a/x2 potential ( part 3)

Ground state of the modified -a/x2 potential ( part 2)

Ground state of the modified -a/x2 potential ( part 1)

Energy Levels of the -1/x^(1/2) Potential

Polynomial fit of the solution to the Thomas-Fermi Equation

Kinetic energy in the Thomas-Fermi model

White dwarf stars equation

The Thomas-Fermi equation V2

The JWKB Method applied to string vibrations

The Variational Principle with a Difference Equation

Electron - electron repulsion by Monte Carlo Method

The Ising Model in One Dimension

Linear Chain of Atoms

The Kronig Penney model

Muonic atom 2P energy level with a finite size nucleus

Muonic atom 2S energy level with a finite size nucleus

Muonic atom with finite size nuclei

Dirac delta function potential

Deep well with a single energy level

THE WKB APPROXIMATION

Energy eigenvalues of a quartic oscillator

Bound states in weak attractive potentials

QUARK CONFINEMENT (u quark) part 1

Barrier reflection for E < V0 (version 2.)

Barrier reflection for E > V0 (a numerical treatment)

Potential barrier

Carbon ground state total energy

Boron ground state total energy

Beryllium ground state total energy

Lithium Total Energy

Lithium Ionization Potential

THE BREIT PAULI EQUATION

Momentum space wave functions (no.1)

Morse Potential- H2 vibrational energy levels

The Stark effect in one dimensional hydrogen

Vibrational energy levels for the hydrogen molecule

The H2+ molecule ion

The X-alpha method -helium atom

Total energies for the 1s2s - 1S state of heliumlike ions

Eigenvalues via Asymptotic Solutions

Nonorthogonal Hartree - Fock

THE ROOTHAAN EQUATIONS

The Linear Variational Method - two STO basis set

Neon atom- a density functional calculation

Lithium atom ,a semi Hartree-Fock calculation

Beryllium - a density functional calculation

Effective potential for lithium

Schrodinger's equation-harmonic oscillator

DIRAC EQUATION-NUMERICAL SOLUTION

Klein Gordon equation

THE HYDROGEN MOLECULE

Effective repulsive potential in Helium

HYDROGENIC ATOMS

QUANTUM OSCILLATOR

THE EXCHANGE INTEGRAL K(1s,2s)

Carbon atom - a density functional calculation

INFINITE AND SEMI INFINITE WELL POTENTIAL

Variational calculation in momentum space

DEUTERON

Double square well potential

SQUARE WELL POTENTIALS

One Dimensional Lithium

One Dimensional Hydrogenic Atom ( Variational treatment)

Neutron energy eigenvalues s and p states

One dimensional helium - part 3

Chemical Kinetics example 1

CALCULUS

Lecture Notes on Calculus Part 2 -Lectures 10,11...

Lecture Notes on Calculus -Part 3 ( Lecture 13...)

Lecture 1, Lecture 2, Lecture 3, Lecture 4 , Lecture 5 , Lecture 6 , Lecture 7, Lecture 8 , Lecture 9, Lecture 10 , Lecture 11 , Lecture 12 , Lecture 13 ,

Complex Variables -Lecture Notes

NUMERICAL ANALYSIS

Boundary Value Problem With Mixed Conditions

Solution of Inhomogeneous Boundary Value Problem

Numerical Inversion of Laplace Transform with the Bromwich Integral

Inversion of Laplace Transform by Post Method

Boundary value problem for ODE

Boundary value problem in one dimension

POISSON?S EQUATION -example 2

POISSON?S EQUATION

LAPLACE EQUATION

Integral Along Branch Cuts

Numerically Inverting the Transfer Function

Numerical Inverse Laplace transform of an oscillator submitted to an impulsive force

Numerical Inverse Laplace transform of an oscillator submitted to a step force

Calculus of Residues Using Complex FORTRAN code

INVERSE LAPLACE TRANSFORM - Part 2

INVERSE LAPLACE TRANSFORM - Part 1

Double precision FORTRAN code for Bessel functions of the second kind Y0 , Y1 , Y2

Double Precision FORTRAN code for the gamma function

FORTRAN code for the gamma function

FORTRAN code for Bessel functions Jn of order 0,1,2

Singular Spherical Bessel Functions - Generating codes

Airy's Differential Equation

EULER'S CONSTANT - GAMMA

Differential equations of fisrt order an first degree

Green's Function for the Heat Equation

Gram-Schmidt Orthogonalization Procedure (17 de julio 2008)

Eigenvalues of an integral equation (16 de julio 2008)

ABEL INTEGRAL EQUATION Part2

VOLTERRA INTEGRAL EQUATIONS OF THE SECOND KIND WITH WEAKLY SINGULAR KERNELS

Triangularization Algorithm for the Determinant

Eigenfrequencies and Normal Modes of Coupled Oscillators by Numerical Methods (Part 2)

Eigenfrequencies of Coupled Oscillators by Numerical Methods (Part 1)

Linear Regression

Example of Gaussian Legendre Integration

Integral equations (example) Problem 100 ,chapter 3, from Methods of Applied Mathematics , Francis B. Hildebrand

Iterative method for Fredholm equation of the second kind

Characteristic values of the Fredholm integral equation -Part 2

Characteristic values of the Fredholm integral equation

Singular Integrals -Version 4-

Singular Integrals-Version 3

Singular Integrals

Helium variation calculation using Gaussian-Legendre Quadrature Integration

Two Dimensional Gaussian Quadrature Integration

Emden?s Equation

Random numbers recursion formula

Building the Logarithmic Table using Taylor series

The Integro-Differential Equation of Volterra

LANGMUIR EQUATION

Applications of the Cayley ?Hamilton Theorem

Solution of the equation d2x/dt2 +c1(dx/dt) +c2 x = c3 sgn(dx/dt)

Dominant Eigenvalue of a Matrix

White dwarf stars equation

Green?s Function of the String Problem (V1)

Fourier sine transform of step function of width b

Fourier sine transform

Numerical solution of the Differential Equation x**2(d2y/dx2)-3.*x(dy/dx) -5.*y=0

Differential Equation of the First Order and Second Degree V 3.0

Differential Equation of the First Order and Second Degree V 2.0

Differential Equation of the First Order and Second Degree

Clairaut Equation V.1

Random number generator (dec 2007)

The Laguerre Equation

Volume of a sphere's octant by Monte Carlo method

Pair of total differential equations in three variables

The Riccati equation

The Binomial Distribution

Linear Pursuit

The Logistic Curve

Calculation of the elliptic function F(phi,k),with phi fixed, k variable

The Elliptic Functions F(phi,k) and E(phi,k)

The Gauss Equation

Cauchy - Euler equidimensional differential equation

Simultaneous Linear differential equations

Planetary orbits -Cartesian coordinates

Associated Legendre Functions

Legendre polynomials

Max-Min with constraint

Max-Min Algorithm

Muonic atom with finite size nuclei

Dirac delta function potential

Deep well with a single energy level

Period formula for the cubic oscillator

Harmonic oscillator with centripetal barrier, the classical and quantum case

Numerical integration of the classical oscillator period formula

HOCB-Harmonic oscillator with centripetal barrier , classical case

Energy eigenvalues of a quartic oscillator

Isotonic oscillator

Projectile motion with air resistance quadratic in speed

Isynchronous motion example 1

PREDATOR PREY POPULATION aug. 2007

Fresnel Integrals (Analytical)

Fresnel integral sin(x**2)

Chebyshev polynomials of the second kind

Chebyshev polynomials of the first kind

Chebyshev Polynomial T2

Definite integral of trigonometric functions// I= $dtheta/(1+a sin(theta) ) , from 0 to 2pi

Improper integrals involving trigonometric functions//Integral of cos(x)dx/(x**2+1.)**2 from -infinity to infinty

Force Free Motion of a Symmetric Top

Two end point problem:The solution of y''+xy'+y=2x that passes through the points (0,1) and (1,0)...

Two-end-point problem y =0 , y''=0 at x= 0;y=0 y'=0 at x=L

Pendulum with linear damping
d^2y/dt^2=-a dy/dt- b sin(y)

Parabolic approximation to the heat equation, T(x,0)=50 (example 2)

Parabolic approximation to the heat equation

Determinant of a Matrix

Three dimensional max-min optimization

Optimization in two dimensions

Optimization of f(x1,x2)=x1**3 + x2**3-2.*x1**2+3.*x2**2-8.

Optimization of f= (x1-sin(x1+x2))**2 +(x2-cos(x1-x2))**2

MATLAB CODES SECTION

SECOND ORDER DIFFERENTIAL EQUATIONS USING MATLAB ODE SOLVER

RC circuit solved with MATLAB ODE15s

Example with MATLAB ODE15s Solver

Emden?s Equation

The Integro-Differential Problem of Volterra (Matlab version)

Kirchoff's Voltage Law (KVL)-Version 2

Kirchoff's Voltage Law (KVL)

Electron repulsion ?Vee- one parameter approximations

Approximation to the exchange energy term K1s2s

The First Painlev項quation

The Second Painlev項quation

The Linear Pursuit Problem

The Logistic Curve

The Duffing equation-MATLAB

Solution of d^2y/dt^2 = -y + (1/6) y^3 +2 sin(3wt)

The Gauss Equation

Alternation of decay and growth

Decay or growth with oscillations

Hermite differential equation : Hermite polynomials

Cauchy Linear Differential Equation (version 1)

Legendre Polynomials (MATLAB version)

Gravitational problem in one dimension

Function with saddle point

The catenary

The cable deflection problem

Eigenvalues of fourth order matrix

Eigenvalues and eigenvectors

Laplace equation

The Predator-Prey Population Equation

The infection equation , dy/dt= k*y(m- y)

Ritz method in one dimension , solution of d^2y/dx^2= - x^2

Fourth order DE , d^4y/dx^4= 24

Second order boundary value problem d2 y/dx2 =(1./8.){32.+2x3 -y*(dy/dx ) }

One dimensional boundary value problem, y''= - x**2 version 3 (solution by iteration)

One dimensional boundary value problem, y''= - x**2

Chemical kinetics (nov 21)

Boltzmann distribution -part 1

THE FOUCALT PENDULUM

Van der Pol equation (nov 18 2006)

RCL with a sinusoidal source

RCL circuit nov14

Stiff Differential equation ,y'=-100y +99 exp(-x)

Stiff differential equation dy/dt= ay**2-by**3

RC circuit example 1

Simple pendulum

Periodic force

Coupled Oscillators

The hydrogen molecule-ion

Gravitational potential

Coupled Oscillators

The Hydrogen Atom-asymptotic method

Schroginger's equation -infinite well

Power method

The heat equation (diffusion equation)

Classic oscillator

Equation of motion , mdv/dt= -mg +kv**2

Damped Oscillator

Gravitational orbits

COMPLEX VARIABLES

Numerically Inverting the Transfer Function

Numerical Inverse Laplace transform of an oscillator submitted to an impulsive force

Numerical Inverse Laplace transform of an oscillator submitted to a step force

Calculus of Residues Using Complex FORTRAN code

INVERSE LAPLACE TRANSFORM - Part 2

INVERSE LAPLACE TRANSFORM - Part 1

Fresnel Integrals (Analytical)

Complex variables (synopsis)

Integral cos^3(3x)dx/((5.-4.*cos(2x))

Definite integral of trigonometric functions// I= $dtheta/(1+a sin(theta) ) , from 0 to 2pi

Improper integrals involving trigonometric functions//Integral of cos(x)dx/(x**2+1.)**2 from -infinity to infinty

Integral of tan(z)dz

Integration of (exp(iz)/z) dz

Integration of dz(5z-2)/( z(z-1))

Complex variable integration of (2x**2- 1) /( x**4+5*x**2+4) dx