Python Calculator

1. Constants and quick calculations¶

scipy.constants knows every physical constant (full list):

A scratchpad, seeded with a photon-energy calculation. Edit it and press play; the value of the last line is displayed:

Or let the slider do the arithmetic. Can this photon break a C-C bond?

2. Unit converter¶

3. Plotting panel¶

A ready-to-edit plotting template. Swap in any function of x; the slider is yours to repurpose:

4. Symbolic window¶

Derivatives, integrals, and equation solving with sympy; results render as typeset math. Each pad is editable:

5. Orbital visualizer¶

Pick quantum numbers; the menus only ever offer valid combinations. Drag to rotate the orbital (blue and red are the wavefunction’s positive and negative lobes):

6. Orbital overlap¶

Bonding starts here: slide two 1s orbitals together and watch their overlap integral $S(d) = e^{-d}\left(1 + d + d^2/3\right)$ grow (distances in Bohr radii). The shaded region is the product $\psi_A \psi_B$ whose integral is $S$:

At $d = 0$ the orbitals coincide and $S = 1$; by $d \approx 8\,a_0$ the overlap is essentially gone. The window where $S$ is a few tenths is exactly where chemical bonds live.

7. One-dimensional Schrödinger solver¶

Pick a potential and get its bound states instantly: energies as horizontal lines, wavefunctions drawn at their own energy (units: $\hbar = m = 1$, hard walls at $x = \pm 4$). To see how the solver works inside, open the numerical Schrödinger lab.

Try the classics: the box gives the $n^2$ ladder, the harmonic well gives perfectly even spacing (the fingerprint of vibrations), the linear well spaces levels like Airy zeros, and the double well pairs levels into tunneling doublets.

8. Numerical integral¶

Define any function and limits in the pad; the plot shades area above the axis in green and below in red, and the value comes from np.trapezoid, the same tool your homework uses:

The green and red areas fight each other: an integral is a signed sum. For probability densities like $|\psi|^2$ the red never appears, which is exactly why they can be interpreted as probabilities.