Find the ground state of the quantum harmonic oscillator. Start by showing that the Hamiltonian from eq
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Find the ground state of the quantum harmonic oscillator. Start by showing that the Hamiltonian from eq
can be ?factorized? similar to (a2 ? b2) = (a ? b)(a + b) in the form
Where?
Show that the Schr?dinger equation is satisfied if (? d/dx + x/?)?0(x) = 0. Show that ?0(x) = Ne?ax2 is such a solution for the right choice of a. Find N such that ?0(x) is normalized. What is the energy of this state?
Transcribed Image Text:
h2 d? 1 2m dx2 +kx 있) V(x) =D Ev (x)
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First show that the Hamiltonian given reduces to the harmonic oscillator Hamiltonian Next suppose dd...View the full answer
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