= μ = 0.5 This problem deals with the vibrational motion of the H2 molecule (reduced mass- amu). The Hamiltonian for this system is: h2 d 1, e2ndxī + 2kx2. 5 pts] By direct substitution of the wa...
= μ = 0.5 This problem deals with the vibrational motion of the H2 molecule (reduced mass- amu). The Hamiltonian for this system is: h2 d 1, e2ndxī + 2kx2. 5 pts] By direct substitution of the wavefunction labelled by the quantum number v, Where k is a constant related to the bond strength. V.(x), in the Schrödinger Equation, show that the wavefunction Ψ(x) = Noe- )' where α = ( corresponds to the ground vibrational state of H2 having energy Bohw, where IS pts] Compute the probability, P, of finding an H2 when it sits in its ground vibrational m k level in the classically forbidden region. 3(5 pts Find a mathematical expression for the location of the nodal planes for the harmonic oscillator eigenfunction W2(x). [5 pts] Prove that the number of nodes in the wavefunction of a Harmonic Oscillator associated with principal quantum number v is exactly v.
= μ = 0.5 This problem deals with the vibrational motion of the H2 molecule (reduced mass- amu). The Hamiltonian for this system is: h2 d 1, e2ndxī + 2kx2. 5 pts] By direct substitution of the wavefunction labelled by the quantum number v, Where k is a constant related to the bond strength. V.(x), in the Schrödinger Equation, show that the wavefunction Ψ(x) = Noe- )' where α = ( corresponds to the ground vibrational state of H2 having energy Bohw, where IS pts] Compute the probability, P, of finding an H2 when it sits in its ground vibrational m k level in the classically forbidden region. 3(5 pts Find a mathematical expression for the location of the nodal planes for the harmonic oscillator eigenfunction W2(x). [5 pts] Prove that the number of nodes in the wavefunction of a Harmonic Oscillator associated with principal quantum number v is exactly v.