Explain the concept of Quantum Phase Estimation (QPE) to a graduate student familiar with linear algebra but new to quantum information theory. Your explanation should bridge the gap between Dirac notation and intuitive understanding. First, describe the mathematical foundation using the inverse Quantum Fourier Transform. Second, provide a concrete analogy involving waves and interference patterns to visualize how the algorithm extracts the eigenvalue. Finally, discuss a specific application in quantum chemistry, such as finding the ground state energy of a molecule.