Schrodinger Equation Calculator

Both formulas put mass in the denominator: the infinite well's Eₙ = n²π²ℏ²/(2mL²) and the harmonic oscillator's Eₙ = (n − 1/2)ℏω (where ω itself is inversely proportional to mass through ω = ℏ/(mL²)) both shrink as Particle Mass grows. Physically, a heavier particle needs less kinetic energy to have the same de Broglie wavelength fit inside the same confinement, so its quantized energy levels sit closer together and lower overall.

Number of Nodes counts how many times the wavefunction crosses zero inside the well or oscillator, and that count is a purely topological property of the quantum state -- the ground state (n=1) always has zero nodes and every higher state adds exactly one, in both potentials modeled here. Particle Mass and Well Width / Char. Length change the ENERGY of each level, not how many times its wavefunction oscillates.

It reuses that field as the oscillator's characteristic length x0, and solves the standard relation x0 = sqrt(ℏ/(mω)) backwards for angular frequency ω, instead of asking for a spring constant directly. This keeps the same two physical inputs -- mass and a length -- meaningful across both potential types, at the cost of not letting you set stiffness and mass independently the way a real spring-mass system would.

This calculator keeps one Quantum Number (n) input that starts at 1 for BOTH potential types, so the harmonic oscillator branch computes energy as (n − 1/2)ℏω rather than the textbook (v + 1/2)ℏω with v starting at 0. Entering n=1 still gives the true ground-state energy of ℏω/2 -- it's labeled with the well's n=1 convention instead of the oscillator's own v=0 convention, so the two branches share one input scale.

No -- Wavelength (λₙ) is the particle's own de Broglie matter wavelength at that energy level, not a photon's wavelength. The photon emitted or absorbed in a transition between levels is described instead by Transition Frequency, which this calculator derives from Energy to Next Level rather than reporting a separate photon wavelength.