Schrödinger Equation Solver

Calculate Quantum Mechanical Properties

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Particle in a Box Calculator

Calculate energy levels and wavefunctions for a particle in an infinite potential well.

Energy and Wavefunction: -

Harmonic Oscillator Calculator

Calculate energy levels and wavefunctions for a quantum harmonic oscillator.

Energy and Zero-point Energy: -

Hydrogen Atom Calculator

Calculate energy levels and properties for the hydrogen atom.

Energy and Radius: -

Understanding the Schrödinger Equation

The Wave Equation

Key concepts of quantum mechanics:

  • Wave-particle duality
  • Probability interpretation
  • Quantum operators
  • Eigenvalue problems

Quantum Systems

Common quantum systems:

  • Particle in a box
  • Harmonic oscillator
  • Hydrogen atom
  • Angular momentum

Quantum Numbers

Understanding quantum numbers:

  • Principal quantum number (n)
  • Angular momentum (l)
  • Magnetic quantum number (m)
  • Spin quantum number (s)

Applications

Schrödinger equation is used in:

  • Atomic structure
  • Molecular bonding
  • Spectroscopy
  • Quantum chemistry
  • Material science

Essential Quantum Mechanical Formulas

Particle in a Box

E_n = (n²h²)/(8mL²)

Where L is box length

Harmonic Oscillator

E_v = hν(v + ½)

Where ν is frequency

Hydrogen Atom

E_n = -13.6 eV/n²

Ground state energy