// multi-utility computation suite · offline · instant · precise
┌──────────────────────────┐
│ [c] calcalyst_ │
│ computation suite │
└──────────────────────────┘
// select a module to initialize
/ search↵ open firstesc close
// adsenseEMPTY_LEADER_SLOT728×90
// keyboard shortcuts
/focus search
Escclear search · close calc
Enteropen first result
↑↓navigate list
?toggle this panel
// adsenseMOBILE_ANCHOR_SLOT320×50
// keyboard_shortcuts
/focus search
↑↓navigate module list
Enter
open first result from search
open highlighted
compute when module is open
compute when focused in a field
Escclose module · clear selection
⌫
sci.quantum-particle-in-box-3D Calculator
Calculates 3D particle-in-a-box energy levels E_nxnynz = h²/(8m)(nx²/Lx² + ny²/Ly² + nz²/Lz²) and lists degenerate states for cubic boxes. In a cubic box, the first excited level is triply degenerate (nx,ny,nz) = (2,1,1) and permutations — degeneracy is lifted when box dimensions differ.
Inputs
L X Nm
Linear measurement. Ensure consistent units: 1 m = 1,000 mm = 3.281 ft.
L Y Nm
Linear measurement. Ensure consistent units: 1 m = 1,000 mm = 3.281 ft.
L Z Nm
Linear measurement. Ensure consistent units: 1 m = 1,000 mm = 3.281 ft.
Nx
Count of items or occurrences.
Ny
Count of items or occurrences.
Nz
Count of items or occurrences.
Results
energy E(nx,ny,nz) (eV)
Sample size or count used in the calculation.
energy E (J)
Sample size or count used in the calculation.
ground state energy E₁₁₁ (eV)
The value at the specified point or condition.
energy ratio E/E_ground
The proportional relationship between two quantities.
E = (ℏ²π²/2m)(nx²/Lx² + ny²/Ly² + nz²/Lz²)
Sample size or count used in the calculation.
degeneracy note
Supplementary information explaining an assumption, caveat, or important context for interpreting the result.