Expectation Value Calculator
Enter complex amplitudes and eigenvalues for up to 10 eigenstates; get the expectation value plus a probability breakdown.
Eigenstates
#
Re(ci)
Im(ci)
λi
Formula Reference
<O> = Σ |ci|² λi
where |ci|² = Re(ci)² + Im(ci)²
Normalization condition: Σ |ci|² = 1
Results
Enter states and click Calculate
Expectation Value <O>
| State | |ci|² | Prob % | λi |
|---|
Sum of |ci|²
Summary
Enter complex amplitudes and eigenvalues for up to 10 eigenstates; get the expectation value plus a probability breakdown.
How it works
- Add up to 10 eigenstates using the "Add State" button.
- For each state, enter the real and imaginary parts of its amplitude c_i.
- Enter the eigenvalue λ_i (the measured value for that eigenstate).
- Click "Calculate" to compute the probabilities |c_i|^2 and the expectation value.
- The tool also checks normalization: the sum of all |c_i|^2 should equal 1.
- Use "Normalize" to rescale all amplitudes so the state is automatically normalized.
Use cases
- Verify homework answers for quantum mechanics problems.
- Explore how changing amplitudes shifts the expected measurement outcome.
- Check that a superposition state is properly normalized.
- Compute the expected energy of a particle in a multi-level potential well.
- Understand spin expectation values for spin-1/2 and higher-spin systems.
- Prototype quantum algorithm outputs before running on hardware.
Frequently Asked Questions
Last updated: 2026-07-23 ·
Reviewed by Nham Vu