Class QuantumHarmonicOscillator

java.lang.Object

org.episteme.natural.physics.quantum.QuantumHarmonicOscillator

public class QuantumHarmonicOscillator
extends Object

Quantum Harmonic Oscillator calculations. *

Reference:
Dirac, P. A. M. (1930). The Principles of Quantum Mechanics. Oxford University Press.

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Field Summary

Fields

Modifier and Type	Field	Description
static final Real	HBAR

Method Summary

Modifier and Type	Method	Description
static Real	angularFrequency(Real springConstant, Real mass)	Angular frequency: ω = sqrt(k/m)
static Real	classicalAmplitude(Real energy, Real mass, Real omega)	Classical amplitude: A = sqrt(2E/(mω²))
static Real	energyLevel(int n, Real omega)	Energy eigenvalues: E_n = ℏω(n + 1/2)
static Real	groundStateEnergy(Real omega)	Ground state energy: E_0 = ℏω/2
static Real	groundStateProbabilityAt0(Real mass, Real omega)	Probability density at x=0 for ground state: |ψ_0(0)|² = sqrt(mω/(πℏ))
static Real	transitionEnergy(int n1, int n2, Real omega)	Transition energy between levels
static Real	zeroPointMotion(Real mass, Real omega)	Zero-point motion: Δx_0 = sqrt(ℏ/(2mω))

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Details

HBAR

public static final Real HBAR

Method Details

energyLevel

public static Real energyLevel(int n,
 Real omega)

Energy eigenvalues: E_n = ℏω(n + 1/2)

angularFrequency

public static Real angularFrequency(Real springConstant,
 Real mass)

Angular frequency: ω = sqrt(k/m)

groundStateEnergy

public static Real groundStateEnergy(Real omega)

Ground state energy: E_0 = ℏω/2

transitionEnergy

public static Real transitionEnergy(int n1,
 int n2,
 Real omega)

Transition energy between levels

classicalAmplitude

public static Real classicalAmplitude(Real energy,
 Real mass,
 Real omega)

Classical amplitude: A = sqrt(2E/(mω²))

groundStateProbabilityAt0

public static Real groundStateProbabilityAt0(Real mass,
 Real omega)

Probability density at x=0 for ground state: |ψ_0(0)|² = sqrt(mω/(πℏ))

zeroPointMotion

public static Real zeroPointMotion(Real mass,
 Real omega)

Zero-point motion: Δx_0 = sqrt(ℏ/(2mω))