Here you are invited to explore the quantum-mechanical harmonic oscillator in more quantitative detail. (a)The groundstate wavefunction of a harmonic oscil lator is proportional to e-ax2/2 . where a depends on the mass and force constant.(i) Normalize this wavefunction; you will need the Integral G1 in the Resource section. (ii) At what displacement is the oscillator most likely to be found in its ground state? Recall that the maximum or minimum of a function f(x) occurs at the value of x for which df/dx= 0. (b) Repeat part (a) for the first excited state of a harmonic oscil lator. for which the wavefunction is proportional to xe-ax2/2
Here you are invited to explore the quantum-mechanical harmonic oscillator in more quantitative detail. (a)The groundstate wavefunction of a harmonic oscil lator is proportional to e-ax2/2 . where a depends on the mass and force constant.(i) Normalize this wavefunction; you will need the Integral G1 in the Resource section. (ii) At what displacement is the oscillator most likely to be found in its ground state? Recall that the maximum or minimum of a function f(x) occurs at the value of x for which df/dx= 0. (b) Repeat part (a) for the first excited state of a harmonic oscil lator. for which the wavefunction is proportional to xe-ax2/2
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Here you are invited to explore the
(i) Normalize this wavefunction; you will need the Integral G1 in the Resource section. (ii) At what displacement is the oscillator most likely to be found in its ground state? Recall that the maximum or minimum of a function f(x) occurs at the value of x for which df/dx= 0. (b) Repeat part (a) for the first excited state of a harmonic oscil lator. for which the wavefunction is proportional to xe-ax2/2
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