Physics

physica

Physica (Latin for natural sciences) provides utilities that simplify otherwise complex and repetitive mathematical expressions in natural sciences.

Its manual provides a full set of demonstrations of how the package could be helpful.

Mathematical physics

The packages/math.md page has more examples on its math capabilities. Below is a preview that may be of particular interest in the domain of physics:

  • Calculus: differential, ordinary and partial derivatives
    • Optional function name,
    • Optional order number or array of order numbers,
    • Customizable "d" symbol and product joiner (say, exterior product),
    • Overridable total order calculation,
  • Vectors and vector fields: div, grad, curl,
  • Taylor expansion,
  • Dirac braket notations,
  • Tensors with abstract index notations,
  • Matrix transpose and dagger (conjugate transpose).
  • Special matrices: determinant, (anti-)diagonal, identity, zero, Jacobian, Hessian, etc.

A partial glimpse:

#import "@preview/physica:0.9.1": *
#show: super-T-as-transpose // put in a #[...] to limit its scope...
#show: super-plus-as-dagger // ...or use scripts() to manually override

$ dd(x,y,2) quad dv(f,x,d:Delta)      quad pdv(,x,y,[2i+1,2+i]) quad
  vb(a) va(a) vu(a_i)  quad mat(laplacian, div; grad, curl)     quad
  tensor(T,+a,-b,+c)   quad ket(phi)  quad A^+ e^scripts(+) A^T integral^T $
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Isotopes

#import "@preview/physica:0.9.1": isotope

// a: mass number A
// z: the atomic number Z
$
isotope(I, a:127), quad isotope("Fe", z:26), quad
isotope("Tl",a:207,z:81) --> isotope("Pb",a:207,z:82) + isotope(e,a:0,z:-1)
$
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Reduced Planck constant (hbar)

In the default font, the Typst built-in symbol planck.reduce looks a bit off: on letter "h" there is a slash instead of a horizontal bar, contrary to the symbol's colloquial name "h-bar". This package offers hbar to render the symbol in the familiar form⁠. Contrast:

#import "@preview/physica:0.9.1": hbar

$ E = planck.reduce omega => E = hbar omega, wide
  frac(planck.reduce^2, 2m) => frac(hbar^2, 2m), wide
  (pi G^2) / (planck.reduce c^4) => (pi G^2) / (hbar c^4), wide
  e^(frac(i(p x - E t), planck.reduce)) => e^(frac(i(p x - E t), hbar)) $
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quill: quantum diagrams

See documentation.

#import "@preview/quill:0.2.0": *
#quantum-circuit(
  lstick($|0〉$), gate($H$), ctrl(1), rstick($(|00〉+|11〉)/√2$, n: 2), [\ ],
  lstick($|0〉$), 1, targ(), 1
)
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#import "@preview/quill:0.2.0": *

#let ancillas = (setwire(0), 5, lstick($|0〉$), setwire(1), targ(), 2, [\ ],
setwire(0), 5, lstick($|0〉$), setwire(1), 1, targ(), 1)

#quantum-circuit(
  scale-factor: 80%,
  lstick($|ψ〉$), 1, 10pt, ctrl(3), ctrl(6), $H$, 1, 15pt, 
    ctrl(1), ctrl(2), 1, [\ ],
  ..ancillas, [\ ],
  lstick($|0〉$), 1, targ(), 1, $H$, 1, ctrl(1), ctrl(2), 
    1, [\ ],
  ..ancillas, [\ ],
  lstick($|0〉$), 2, targ(),  $H$, 1, ctrl(1), ctrl(2), 
    1, [\ ],
  ..ancillas
)
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#import "@preview/quill:0.2.0": *

#quantum-circuit(
  lstick($|psi〉$),  ctrl(1), gate($H$), 1, ctrl(2), meter(), [\ ],
  lstick($|beta_00〉$, n: 2), targ(), 1, ctrl(1), 1, meter(), [\ ],
  3, gate($X$), gate($Z$),  midstick($|psi〉$)
)
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