Zero-Point Ladder

Plate 40 speaks for itself: “Even at rest, never still.”

The Physics

A quantum harmonic oscillator has evenly spaced energy levels, and the lowest is not zero: even in its ground state it keeps ħω/2 of zero-point energy.

E_n = ħω (n + ½)

• E_n: energy of level n, J
• ħ: reduced Planck constant, 1.054571817×10⁻³⁴ J s
• ω: angular frequency, rad s⁻¹
• n: quantum number 0, 1, 2, …, dimensionless

Even at n = 0 the energy is ħω/2. Rungs are evenly spaced by ħω.

Sources

• D. J. Griffiths, Introduction to Quantum Mechanics, 3rd ed., §2.3.

On the poster

Plate 040, “Zero-Point Ladder”: the pixel-art plate with its slogan “Even at rest, never still.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.