Python Calculator - Quantum Mechanics for Chemistry

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. 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.

5. Symbolic window¶

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

6. Orbital visualizer¶

Pick quantum numbers (the menus only ever offer valid combinations). The first plot is a 2D cross-section of the orbital in the xz-plane, with blue and red marking the wavefunction’s positive and negative lobes. Below it, the radial view shows the radial function $R_{nl}(r)$ and the radial distribution $P(r) = r^2 R^2$ , and reports the most probable radius, the mean radius $\langle r\rangle$ , and the node count.

7. Orbital overlap¶

Bonding starts here. The overlap integral $S = \int \psi_A \psi_B\,d^3r$ measures how much two atomic orbitals share the same region with the same sign. Pick an orbital on each center, slide them together, and watch the overlap. The left panel shows both orbitals along the bond ( $z$ ) axis; the right panel is the product $\psi_A\psi_B$ whose integral is $S$ . Try 1s with 2p_x to see an overlap that cancels to zero by symmetry.

The window where $|S|$ is a few tenths is exactly where chemical bonds live. Pushing the nuclei together raises $|S|$ , while a mismatch in orbital symmetry drives it to zero no matter how close they get.

8. 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.