Show that the hydrogen wave function Ψ211 is normalized
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Show that the hydrogen wave function Ψ211 is normalized
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- The normalised wavefunction for an electron in an infinite 1D potential well of length 89 pm can be written:ψ=(-0.696 ψ2)+(0.245 i ψ9)+(g ψ4). If the state is measured, there are three possible results (i.e. it is in the n=2, 9 or 4 state). What is the probability (in %) that it is in the n=4 state?Show the relation LxL = iħL for the quantum mechanical angular momentum operator LBy taking the derivative of the first equation with respect to b, show that the second equation is true. Use this result to determine △x and △p for the ground state of the simple harmonic oscialltor.
- Show that the following function Y(0,9)= sin 0 cos e eiº is the solution of Schrödinger 1 1 equation: sin 0 21 sin 0 00 Y(0,0)= EY (0,9) and find the sin 0 dp? energy, E.Solve the time-independent Schrödinger equation and determine the energy levels and the wave function of a particle in the potential a? V (x) = Vol a + 2r2 with a = const.Particle of mass m moves in a three-dimensional box with edge lengths L1, L2, and L3. (a) Find the energies of the six lowest states if L1 =L, L2 = 2L, and L3 = 2L. (b) Which if these energies are degenerate?
- An electron is confined between two perfectly reflecting walls separated by the distance 12 x 10-11m. Use the Heisenberg uncertainty relation to estimate the lowest energy that the particle can have (in eV).a 4. 00, -Vo, V(z) = 16a 0, Use the WKB approximation to determine the minimum value that V must have in order for this potential to allow for a bound state.Show that normalizing the particle-in-a-box wave function ψ_n (x)=A sin(nπx/L) gives A=√(2/L).