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The eigenstates of a one-dimensional harmonic oscillator are described by the orthonormal eigenfunctions Ho (y) = 1 H₁ (
Posted: Mon Jul 11, 2022 12:44 pm
by answerhappygod
- The Eigenstates Of A One Dimensional Harmonic Oscillator Are Described By The Orthonormal Eigenfunctions Ho Y 1 H 1 (58.69 KiB) Viewed 36 times
The eigenstates of a one-dimensional harmonic oscillator are described by the orthonormal eigenfunctions Ho (y) = 1 H₁ (y) = 2y where n denotes a quantum number labeling a state of the oscillator and Hn (y) with y = mw V ħ H₂ (y) = 4y² - 2 H3 (y) = 8y³ - 12y H4 (y) H5 (y) 32y 160y³ + 120y 16y4 - 48 y² + 12 If a harmonic oscillator is found in a state · (-²²) (a) What is the probability that its energy is five times the ground state energy? (b) Calculate the average energy of the system. (c) Determine the expectation value of the system's position. Un (x) (y) = N(y¹ - 1) exp = (mw) & H₂ ( √mw x) exp (- 17h1 x²) x are Hermite polynomials,