Probability Amplitude Calculator
Calculate quantum probability amplitudes, Born rule probabilities, phase angles, and normalization.
Inputs
Results
Probability |α|²
1
Magnitude |α|
1
Phase Angle
53.13°
Normalized Re0.6
Normalized Im0.8
Inner Product ⟨α|α⟩1
How to Use This Calculator
- Enter the Real Part (Re) and Imaginary Part (Im) of the quantum probability amplitude α.
- The Probability |α|² is the Born rule result — the actual measurable probability of finding the system in this state.
- Magnitude |α| must be ≤ 1 for a normalized amplitude; if it exceeds 1, renormalize the state vector first.
- Phase Angle (°) represents the relative phase, which matters for quantum interference but not for individual measurements.
- Use Normalized Re and Im outputs when you need the unit-normalized components for superposition calculations.
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Formula
P = |α|² = Re² + Im²Related Calculators
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