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General description:
- This widget allows performing simple numerical calculations specialized
for physical quantities. It incorporates a substantial number of physical
units and fundamental constants expressed in atomic units (a.u.), which
are defined such that e=ℏ=me=1.
- Mathematical expressions can be introduced in the upper window to yield
their numerical values as comments in the lower window when clicking
the "calculate" button. Expressions are separated by ";" deliminters,
with no ";" necessary for the last of them. Comments can be introduced
starting with "//" and finishing at the end of the current line. The
generated list of expressions along with their values have a format
compatible with the input, so it can be directly calculated again or
modified, copied in the upper window, and recalculated by clicking "calculate".
- Each expression can involve numerical constants or previously defined
variables. The calculation fails when an undefined variable is used.
Predefined variables are listed below in the form of Mathematical and
Physical constants. A reduced set of Mathematical functions is also
available as listed below.
Single-argument functions (complex numbers are supported):
- ln=log, exp, sin, cos, tan, asin, acos, atan, Re, Im, arg, conj
- abs=mod=ABS, sqr, sqrt, sinh, cosh, tanh
- Bessel: J0,J1,J2,J3, Y0,Y1,Y2,Y3, j0,j1,j2,j3, y0,y1,y2,y3
- Struve: L_1,L0,L1
- Legendre polynomials: P00,P10,P11,P20,P21,P22.
- Airy functions: Ai,Bi,Aip,Bip
- Gamma, erf, fact(n)=n!
- Specific functions for free electrons: gamma(E) and v(E) give the
Lorentz factor and the velocity for an electron moving with velocity E
in a.u. One can use, for example, "v(100*keV)" to calculate the velocity
of a 100 keV electrons.
Mathematical constants:
- pi=Pi=PI is π
- e=E is Euler's number
- I is the imaginary unit
Physical constants:
- Different units expressed in a.u. (e.g., "nm" gives the numerical value
"18.8973", which is 1 nm in a.u.): nm, m, s, kg, J, W, N, C, T, A, V
- eV, keV, THz, cm1
- Constants in a.u.: c, kB, mp, amu, Na (Avogradro), G (gravitation)
- Constants in MKS: c0, kB0, G0, hbar, epsilon0
- Miscellaneous: lam1 (wavelength in nm at 1 eV photon energy)
Miscellaneous:
- decompose(integer): prime number decomposition
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