Quantum Harmonic Oscillator Overlay

🧪 Quantum Harmonic Oscillator Overlay
A visual model of price behavior using quantum harmonic oscillation principles

📜 Indicator Overview
The Quantum Harmonic Oscillator Overlay applies concepts from both classical physics (harmonic motion) and quantum mechanics (energy states) to model and visualize how price orbits around a central trend line. It overlays a Linear Regression line (representing the “mean position” or ground state of price) and calculates surrounding energy levels (σ-zones) akin to quantum shells that price can "jump" between.

This indicator is particularly useful for visualizing mean reversion, volatility compression/expansion, and momentum-driven price breakthroughs.

🧠 Core Concepts
Linear Regression Line (LSR): This is the calculated center of gravity or equilibrium path of price over a user-defined period. Think of it like the lowest energy state or central axis around which price vibrates.

Standard Deviation Zones (σ-levels):

1σ: The majority of normal price activity; within this range, price tends to fluctuate if in balance.

2σ: Indicates volatility or possible breakout pressure.

3σ: Represents extreme movement — a phase shift in energy, potentially leading to reversal or continuation with higher momentum.

Quantum Analogy: Just like in a quantum harmonic oscillator, particles (here, prices) move probabilistically between discrete energy states. The further the price moves from the center, the more "energy" (momentum, volume, volatility) is implied.

⚙️ Input Parameters
Setting Description
Linear Regression Length The number of bars used to calculate the regression trend (default 100). Affects the central path and responsiveness.
σ Multipliers (1σ, 2σ, 3σ) Determine how far each band is from the regression line. Adjusting these can highlight different price behaviors.
Show Energy Level Zones Toggle visibility of the colored bands around the regression line.
Show LSR Center Line Toggles visibility of the white Linear Regression line itself.

🎨 Visual Components
Color Zone Interpretation
✅ Green ±1σ Normal oscillation / mean reversion area. Ideal for range-bound strategies.
🟧 Orange ±2σ Warning zone; price may be gaining momentum or volatility.
🔴 Red ±3σ High-momentum state or anomaly. These regions may imply trend exhaustion, reversals, or breakouts.

White Line: The LSR — the average trajectory of the price movement.

Pink Dots: Appear when price exceeds Zone 3 (outside ±3σ) — a signal of extreme behavior or a possible regime shift.

📈 How to Use This Indicator
1. Detect Overextensions
When price touches or breaches the 3σ zone, it is likely overextended. This can be used to anticipate potential snapbacks or strong breakout trends.

2. Identify Mean Reversion Trades
If price exits the 2σ or 3σ zones and returns toward the center line, this signals a likely mean reversion setup.

3. Volatility Compression or Expansion
Flat zones between σ levels suggest calm markets; widening bands suggest expanding volatility.

4. Use with Confirmation Tools
Combine with momentum oscillators (MACD, RSI) or volume-based signals to confirm reversals or continuation outside Zone 3.

🔮 Philosophical Note
This indicator embodies the metaphor that the market behaves like a quantum oscillator — price particles exist in a probabilistic field and jump between discrete zones of volatility and energy. Tracking these transitions allows the trader to see price behavior as rhythmic, wave-like, and multidimensional rather than purely linear.