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2. Consider the wavefunction for the ground state of the quantum oscillator given by Vo(x) = C,e¬ax² Using the quantum harmonic potential U(x) = mw²x², write the complete Schrödinger equation and: (a) Determine the value of a, Co, and energy E. (b) Calculate (x), (x²), and Ax. (c) Calculate (p), (p²), and Ap. Show that the product of Ax and Ap follows the uncertainty principle.

2. Consider the wavefunction for the ground state of the quantum oscillator given by Vo(x) = C,e¬ax² Using the quantum harmonic potential U(x) = mw²x², write the complete Schrödinger equation and: (a) Determine the value of a, Co, and energy E. (b) Calculate (x), (x²), and Ax. (c) Calculate (p), (p²), and Ap. Show that the product of Ax and Ap follows the uncertainty principle.

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2. Consider the wavefunction for the ground state of the quantum oscillator given by Yo(x) = Coe-ax² Using the quantum harmonic potential U (x) = ÷mw²x², write the complete Schrödinger equation and: (a) Determine the value of a, Co, and energy E. (b) Calculate (x), (x²), and Ax. (c) Calculate (p), (p²), and Ap. Show that the product of Ax and Ap follows the uncertainty principle.
Transcribed Image Text:2. Consider the wavefunction for the ground state of the quantum oscillator given by Yo(x) = Coe-ax² Using the quantum harmonic potential U (x) = ÷mw²x², write the complete Schrödinger equation and: (a) Determine the value of a, Co, and energy E. (b) Calculate (x), (x²), and Ax. (c) Calculate (p), (p²), and Ap. Show that the product of Ax and Ap follows the uncertainty principle.
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