10. Consider an isotropic three-dimensional harmonic oscillator for a particle of mass u and the Hamiltonian H = 1 === P² + 1/2 HW³R 2μ Where P and R are the three-dimensional momentum and position operators. (a) Find the eigenvalues and the eigenfunctions of the Hamiltonian and the degrees of degeneracy for the energy levels.

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Q: You are given a free particle (no potential) Hamiltonian Ĥ = dependent wave-functions V₁(x, t)…

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Q: What is the degeneracy of a molecule rotating with J = 3?

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Q: Which of these choices is the expectation value of momentum squared p2 for a particle in the state n…

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Q: 3. Verify that the wave function y(x) = Ae (ku) ¹/² x² /(2n)] (where A, m, and k are all constants)…

A: The Schrodinger statement is given by  H^ψ(x) = Eψ(x) Where, H^ is the Hamiltonian operator…

Q: Determine the commutator of the operators a and at. [₁,₂] = Â₁Â₂ - Â₂Î₁ at = (x- ip) √2 a = (X + ip)…

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Q: What is the degeneracy of a molecule rotating with 1 = 3? With 1=4?

A: Conclusion :  The degeneracy of a molecule rotating with I=3 is 7 and with I=4 is 9 Explanation:Step…

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Techniques and applications of quantum theory

Quantum theory, often known as quantum physics, is the foundation of modern physics and encompasses the nature and behavior of matter and energy at the atomic and molecular levels. As the exact nature and behavior of atomic and subatomic particles are impossible to determine, the laws of classical physics do not apply to this discipline. As a result, quantum field theory is primarily based on assumptions and probabilities.