DEMO: First Steps with Python

The page has five stations, and each one introduces exactly one library at the moment it becomes useful: physical constants, then arrays and plots, then symbolic math.

1. Python as a scientific calculator¶

Our first import: scipy.constants knows every physical constant, so you never mistype one (full list). One line of code, and $h$, $c$, $e$, $k_B$, $N_A$ are all at your fingertips:

A green laser pointer emits 532 nm light. What is the energy of one of its photons? Type the formula $E = h c / \lambda$ almost exactly as you would write it:

Joules are inconvenient at the atomic scale, so chemists quote photon energies in electron volts (divide by the electron charge) or kJ/mol (multiply by Avogadro’s number). Unit conversion is just arithmetic:

A mole of green photons carries about 225 kJ, and a typical C-C single bond costs 347 kJ/mol. Can light break a bond? Drag the slider and find out. Making an interactive control is one line of code:

Notice the chemistry hiding in this toy: visible light cannot touch a C-C bond, but ultraviolet light below roughly 345 nm can. That is why UV radiation damages molecules and sunscreen exists.

2. The de Broglie wavelength, in three lines¶

The same calculator settles a chapter question: why do electrons diffract but baseballs do not? Compute $\lambda = h / mv$ for both. For the electron we use its speed in the ground state of the Bohr model Bohr, 1913, $v \approx 2.19 \times 10^6$ m/s:

3. Functions: the hydrogen spectrum¶

When a formula gets used more than once, wrap it in a function. The Rydberg formula predicts every line hydrogen emits when an electron falls from level $n_{hi}$ to $n_{lo}$:

Now the function powers a live energy-level diagram. Pick a series and an upper level; the diagram draws the transition and colors the emitted photon:

Gray arrows mean the photon lies outside the visible window. Only the Balmer series lands in it, which is why hydrogen discharge tubes glow red-pink: you are looking mostly at the 656 nm line you computed above.

4. Plotting: blackbody radiation¶

Two more imports, and they are the workhorses of all scientific Python: numpy handles arrays of numbers, and matplotlib turns them into figures.

Planck’s law Planck, 1901 started quantum mechanics. Typed as code, it is three lines:

The default 5800 K is the surface of the Sun: its peak sits right in the visible band (evolution is not a coincidence). Cool the slider to 3000 K, a light bulb filament, and watch the peak slide into the infrared, which is why incandescent bulbs waste most of their energy as heat.

5. Symbolic math: let the computer do calculus¶

Our final import is sympy, an entire computer algebra system:

The dashed “peak” line obeys Wien’s law, $\lambda_{max} T = b$. In 1900 deriving it took real work; sympy differentiates Planck’s law and finds the root for you. One standard physics trick first: substitute the dimensionless variable $x = hc / \lambda k_B T$, so Planck’s law becomes a clean scale-free shape $x^5 / (e^x - 1)$ and every temperature collapses onto one curve:

That output is not a decimal: sympy solved the transcendental equation exactly, in terms of the Lambert W function. Turned into numbers, it hands us Wien’s constant:

The result matches the dashed line in the plot above and scipy’s tabulated constant to four digits. You will use the same maximize-by-differentiating trick later to locate maxima of probability densities.

6. Complex numbers: a 30-second preview¶

Quantum wavefunctions are complex-valued, so Python treats complex numbers as first-class citizens (1j is the imaginary unit). Take $z = 1 + \sqrt{3}\,i$:

The quantity $z z^* = |z|^2$ is exactly how probability densities are built from wavefunctions in Chapter 3.