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indigojoker
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I was just wondering what the difference was in the 1-D simple harmonic oscillator in the Heisenberg picture versus the Schrodinger picture?
A 1-D simple harmonic oscillator is a physical system that exhibits periodic motion around an equilibrium point, with a restoring force proportional to its displacement from that point.
The equation of motion for a 1-D simple harmonic oscillator is x(t) = A*cos(ω*t + φ), where x is the displacement from equilibrium, A is the amplitude, ω is the angular frequency, and φ is the phase constant.
The period of a 1-D simple harmonic oscillator is equal to 2π divided by its angular frequency, T = 2π/ω. This means that the period and frequency are inversely proportional to each other.
The potential energy function for a 1-D simple harmonic oscillator is given by U(x) = 1/2*k*x^2, where k is the spring constant and x is the displacement from equilibrium. This potential energy function represents the energy stored in the system due to the spring's elastic properties.
The mass of a 1-D simple harmonic oscillator affects its motion by changing its natural frequency. A larger mass will result in a lower natural frequency and longer period, while a smaller mass will result in a higher natural frequency and shorter period. However, the amplitude and phase of the oscillation will remain unchanged.