Quantum Harmonics – Equations & Interpretations
🔁 Harmonic Oscillator Energy Levels#
$$ E_n = \left(n + \frac{1}{2}\right)\hbar \omega $$
- ( n ): Quantum number (0, 1, 2, ...)
- ( \omega ): Angular frequency
- ( \hbar ): Reduced Planck constant
🧠 Triadic Interpretation#
- Object: Oscillator
- Attribute: Frequency ( \omega )
- Condition: Quantum number ( n )
Lab 4: Harmonic Memory — Equations#
1. Harmonic Memory State#
Define a memory state encoded in harmonic basis:
$$ |M\rangle = \sum_{n=0}^{\infty} c_n |H_n\rangle $$
Where ( |H_n\rangle ) are harmonic eigenstates and ( c_n ) are memory coefficients.
2. Resonant Recall Operator#
Introduce a recall operator ( \hat{R} ) that retrieves harmonic memory:
$$ \hat{R} |M\rangle = \sum_{n=0}^{\infty} c_n \hat{R} |H_n\rangle $$
Assuming ( \hat{R} |H_n\rangle = r_n |H_n\rangle ), we get:
$$ \hat{R} |M\rangle = \sum_{n=0}^{\infty} r_n c_n |H_n\rangle $$
3. Harmonic Overlap Metric#
Define a memory fidelity metric ( \mathcal{F}_H ):
$$ \mathcal{F}H = |\langle M{\text{stored}} | M_{\text{retrieved}} \rangle|^2 $$
4. Triadic Harmonic Tensor#
Construct a triadic tensor ( T_{mnk} ) for harmonic memory propagation:
$$ T_{mnk} = \langle H_m | \hat{R}_n | H_k \rangle $$
Encodes memory transitions across harmonic modes.
🎭 Mythic Echo#
“The ladder of energy is carved from silence.”
— Nawder Loswin