21. Schrödinger Equation in Curved Spacetime
21. Schrödinger Equation in Curved Spacetime (Quantum Gravity) Equation: $$ i\hbar \frac{\partial \Psi}{\partial t} = \left( -\frac{\hbar^2}{2m} \nabla^2 + V + \frac{1}{2} m \omega^2 r^2 \right) \Psi $$ Relational Explanation: The Schrödinger Equation in Curved Spacetime extends the traditional Schrödinger equation to account for the effects of spacetime curvature on quantum particles. This formulation is essential for understanding quantum phenomena in strong gravitational fields, such as those near black holes or in the early universe. Quantum Mechanics (QM): Schrödinger Equation: Describes the time evolution of a quantum system's wavefunction \( \Psi \). Wavefunction (\( \Psi \)): Encapsulates the probability amplitude of finding a particle in a given state. ...