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2m (ax2 a) Prove that the time independent Schrodinger equation is satisfied by the following wavefunction. NTL' sin L sin Where n and q are positive nonzero integers and ng is normalized. b)What is the energy of the wavefunction from part a? c)What is the degeneracy of the ground state and first two excited states of this system?

2m (ax2 a) Prove that the time independent Schrodinger equation is satisfied by the following wavefunction. NTL' sin L sin Where n and q are positive nonzero integers and ng is normalized. b)What is the energy of the wavefunction from part a? c)What is the degeneracy of the ground state and first two excited states of this system?

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Problem 3 Consider the 2-D particle in a box, the particle in a square. This particle is trapped in a square region of area L?, with the bottom left corner of the square at the origin. The potential inside the square is zero so the Hamiltonian inside the square is
Transcribed Image Text:Problem 3 Consider the 2-D particle in a box, the particle in a square. This particle is trapped in a square region of area L?, with the bottom left corner of the square at the origin. The potential inside the square is zero so the Hamiltonian inside the square is
* - 2m (dr² + əya) . ду? a) Prove that the time independent Schrodinger equation is satisfied by the following wavefunction. sin L sin L (E) Where n and q are positive nonzero integers and g is normalized. b)What is the energy of the wavefunction from part a? c)What is the degeneracy of the ground state and first two excited states of this system? d)Imagine a composite state made from the wavefunctions in part a V = c1 W1,1 + C263,4 where |c|2 + |c2|? = 1. i)A measurement of the energy of V can yield what possible results? ii)Find (E) for the state V.
Transcribed Image Text:* - 2m (dr² + əya) . ду? a) Prove that the time independent Schrodinger equation is satisfied by the following wavefunction. sin L sin L (E) Where n and q are positive nonzero integers and g is normalized. b)What is the energy of the wavefunction from part a? c)What is the degeneracy of the ground state and first two excited states of this system? d)Imagine a composite state made from the wavefunctions in part a V = c1 W1,1 + C263,4 where |c|2 + |c2|? = 1. i)A measurement of the energy of V can yield what possible results? ii)Find (E) for the state V.
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