Calculate the Energy of a Particle in a Three-Dimensional Rectangular Box

Particle in a Box Energy Calculator

Enter mass in kilograms (kg).
Enter length in meters (m).
Enter length in meters (m).
Enter length in meters (m).
Must be a positive integer (1, 2, 3...).
Must be a positive integer (1, 2, 3...).
Must be a positive integer (1, 2, 3...).

Calculation Result:

The energy of the particle (E) is: Joules

Unlock the secrets of quantum mechanics with our free online Energy of Particle in a 3D Box Calculator. Quickly determine the quantized energy levels for particles confined within a rectangular potential well. This tool is ideal for students, educators, and physicists exploring fundamental concepts like wave functions and boundary conditions in quantum systems.

Formula:

The energy levels (E) of a particle in a three-dimensional rectangular box are given by the formula:

E = (h² / 8m) × ((nx² / Lx²) + (ny² / Ly²) + (nz² / Lz²))

  • E: Energy of the particle (Joules)
  • h: Planck's constant (6.626 × 10-34 J·s)
  • m: Mass of the particle (kilograms)
  • nx, ny, nz: Quantum numbers for each dimension (positive integers: 1, 2, 3, ...)
  • Lx, Ly, Lz: Lengths of the box along the x, y, and z axes, respectively (meters)

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