I make extensive use of Mathcad in my teaching. and for computationally nondemanding calculations in my research as well. Below I give links to download a number of the files, which are currently in Mathcad2001 format. I arrange them by topic. I cannot offer support for these documents but would be happy to receive any comments or criticisms, most especially, any errors in the document. Kevin Lehmann
Physical Constants: This file needs to be “Referenced” at a beginning of a large number of the files that follow. It defines the standard physical constants as well as the standard SI units symbols, including the standard prefixes, i.e. things like mJ for 0.001 Joule. One warning is the “e” is redefined as the quantum of charge and thus no longer functions as Euler’s number. As a result, exp(x) still works but e^x does not.
Quantum Mechanics and Spectroscopy:
Airy function (wavefunction for a particle in a constant force potential)
Anharmonic Oscillator subject to frequency sweep
Atomic Mass Table List of standard atomic weight values for different elements
Isotope Mass Table List of atomic mass values for different isotopic forms
Defines Mathcad functions that calculate the ClebschGordon Coefficients, Wigner 3J, and 6J Symbols.
Diatomic Duham Expansion. Gives the relationship between the potential expansion as power series around the equilibrium position and the Dunham expansion of the term values as power series in vibrational and rotational quantum numbers.
Diatomic Rovibrational Spectrum. Develops least squares fit routines for fitting the vibrational spectrum of a diatomic molecule (or parallel band of a linear molecule). Sample input data is found in the CO_v1_data and CO_v2_data.
Diatomic Molecule Spectrum Intensities. This discusses the intensity and shape of spectral lines in a Diatomic rovibrational spectrum. Includes relationship of line strength to the derivative of the dipole moment with respect to the bond length.
Direction Cosine Matrix Elements. This provides Mathcad functions that calculate the direct cosine matrix elements.
Time evolution of Free Particle Wavefunction. This calculates how an initial minimum uncertainty wavepacket of a free particle spreads in time. It demonstrates that the spread in width can be quantitatively accounted for by the initial spread in momentum.
Harmonic Oscillator Wavefunctions. This defines a Mathcad routine to calculate the Harmonic Oscillator functions. It is stable to high quantum number due to use of recursion relationship.
Morse Oscillator. This provides an analysis of the classical and quantum treatments of a Morse Oscillator, including defining a Mathcad Function for the eigenfunctions.
NumerovCooley Integration of Wavefunctions. This demonstrates the use of the NumerovCooley Integration method and defines functions that can be used to do this in one step.
Point Group Calculator. This automates the calculation of the irreducible representations for sets of electronic orbitals or for nuclear displacements (vibrations).
Resonance. This demonstrates Quantum Resonance by the example of a particle trapped behind a square well barrier.
RKR Inversion. This shows how the vibrational energy and rotational constant for each vibrational level can be used to extract the shape of the potential. Spectroscopic data from CO is used for an example calculation.
Spherical Harmonics. Tutorial document about spherical harmonic functions.
Step Barrier. Displays the transmission and reflection of a barrier step potential as a function of energy.
Moments of Inertia Calculation. This document defines the moment of inertia tensor, rotational constants, and principle axis system from a set of atomic Cartesian coordinates. Also includes functions to construct Cartesian coordinates from a set of internal coordinates (bond lengths, bond angles, torsion angles, etc).
Curve of Growth Corrections. This calculates the apparent deviations from the Beer’s Law caused by finite instrumental width compared to the width of spectral lines.
Statistics:
AD Bias. Because an Analog to Digital converter has a finite resolution (single bit size) without input noise there will be an error of up to one half the input voltage corresponding to a single bit. This worksheet demonstrates how quickly the maximum error decreases when we have Gaussian random noise on the input.
Binomial Distribution Function. Tutorial document on the Binominal Distribution, its uses, and the Mathcad functions for this distribution.
Gaussian Distribution Function. Tutorial document on the Gaussian or Normal Distribution, its uses, and the Mathcad functions for this distribution.
Poisson Distribution Function. Tutorial document on the Poisson Distribution functions, their uses, and the Mathcad functions for these distributions.
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Mean Vs. Median. Compares the use of the Mean and Median values of finite data sets as measures of the population from which the data is drawn. It is shown that for populations with outliers, the median will have lower fluctuations.
Rejection of Data. Demonstrates, by numerical simulation, how statistical tests can be used to provide objective statistical criteria to remove outliers from a data set, thus making the predictions more reliable.
Linear Regression. Discussion of linear correlation and how it can be quantified and tested for using Mathcad functions.
Linear Least Squares Fitting. Presents an analysis of fitting data to functions that are linear in unknown parameters. Unlike the built in Mathcad functions that do the same, the functions defined herein allow to weighted least squares fitting and also produce the variances and covariances of the fit parameters.
Optics:
Air Index of Refraction
BaF2 Index of Refraction
CaF2 Index of Refraction
Fused Silica Index of Refraction
Sapphire Index of Refraction
Light beam propagation template. This defines the “ABCD” matrices for different optical elements and other functions useful in propagating Gaussian beams and calculation of the TEM00 modes of optical cavities.
Model of Dielectric Mirror. Uses Matrix methods to calculate the reflectivity and transmission of a mirror made of stacks of dielectric material with alternate high and low index of refraction.
Fresnel Equations for Reflection and Transmission Amplitudes
Statistical Mechanics:
Thermodynamics of a Polyatomic molecule from spectroscopic data
Molecular Dynamics Simulation of a 2Dimensional of atoms held together by LenardJones potentials.
MonteCarlo Simulation of a 2Dimensional model of absorbateabsorbate interactions on a surface.
A site with links to several sites with Chemsitry related Mathcad worksheets: Mathcad Applications in Chemistry
