The Quantum Pendulum Clock · AI Generator #GEN-96975F4A

Physics · quantum-mechanics

Problem

A revolutionary quantum clock uses a charged particle of mass m=9.11×10−31  kgm = 9.11 \times 10^{-31}\;\text{kg} and charge q=1.60×10−19  Cq = 1.60 \times 10^{-19}\;\text{C} confined in a one-dimensional harmonic potential well. The particle oscillates between two electrodes separated by distance L=2.0×10−9  mL = 2.0 \times 10^{-9}\;\text{m}, with the potential minimum at the center. The clock's "tick" occurs when the particle transitions from the first excited state (n=1n=1) to the ground state (n=0n=0), emitting a photon. To ensure precise timekeeping, the clock is designed so that the quantum uncertainty in the particle's momentum when in the ground state equals exactly 14\frac{1}{4} of the classical momentum amplitude of a classical oscillator with the same total energy as the quantum ground state. (a) Find the angular frequency ω\omega of the harmonic oscillator. (b) Calculate the wavelength of the photon emitted during each "tick" of the clock. Given: ℏ=1.055×10−34  J⋅s\hbar = 1.055 \times 10^{-34}\;\text{J·s}, c=3.00×108  m/sc = 3.00 \times 10^8\;\text{m/s}

Related theory

Browse the problem library