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Portable Eigenmath 137 Free Download

01.30.2010 · Posted in Education, Portable Application
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eigenmath

Eigenmath is a free, easy to use, no installation, multiplatform computer algebra system, written in the C programming language.

It facilitates the manipulation of mathematical expressions in symbolic form. For example, it can assist in solving algebra and calculus problems. The application includes a great deal of math functions.

This application eases the use if mathematical expressions in symbolic form, eligible for students in college and university.

For example script, quantum harmonic oscillator

# “Harmonic oscillator” is the generic term for a system that has potential

# energy V proportional to x squared.

#

# For total energy E, kinetic energy K and potential energy V we have

#

# E = K + V

#

# For QHO the equivalent Schroedinger equation is:

#

# 2 2 2

# (2n + 1) psi = -d psi / dx + x psi

#

# This differential equation can only be solved for integer values of n.

# The fact that n must be an integer is in agreement with physical reality:

# the total energy of a QHO system is quantized.

#

# The solution to the above equation is

#

# 2

# psi(n,x) = exp(-1/2 x ) H (x)

# n

#

# H (x) is the nth Hermite polynomial in x.

# n

# Define the wave function.

psi(n) = exp(-1/2 x^2) hermite(x,n)

# We want to show that psi does indeed solve the Schroedinger equation.

# We start by defining the energy functions E, K and V.

E(n) = (2 n + 1) psi(n)

K(n) = -d(d(psi(n),x),x)

V(n) = x^2 psi(n)

# Text strings are displayed when the script runs.

“Checking E = K + V for n = 0 to 10″

# The check function stops with an error message if its argument is false.

for(n, 0, 10, check(E(n) = K(n) + V(n)))

# If we get here then everything worked out, print OK.

“OK”

# After a script runs, all of its functions and variables are available for

# immediate mode calculations.

# For example, try entering K(10).

Another example scripts:

  • hydrogen wavefunctions
  • gamma matrix algebra
  • free particle dirac equation
  • maxwell in tensor form
  • static spherical metric
  • bondi metric
  • circular polarization
  • elliptical polarization
  • vector calculus demo
  • rotation matrix demo

[download id="124" format="6"]

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