Find the ground state of the quantum harmonic oscillator Start by showing that the Hamiltonian from eq can be factorized similar to (a 2 b 2 ) (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 c...

Find the ground state of the quantum harmonic oscillator. Start by showing that the Hamiltonian from eq

Question:

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?

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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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ISBN: 978-1107016651

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Question Posted: Jan 21, 2019 10:27 AM

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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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