Write out the hydrogen wave functions cnℓmℓ for φ nℓmℓ values of (2, 1,-1), (2, 1, 0), and (3, 2, -1).
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Write out the hydrogen wave functions cnℓmℓ for φ nℓmℓ values of (2, 1,-1), (2, 1, 0), and (3, 2, -1).
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- How might I appropriately answer 10.1?19.7 The variation principle can be used to formulate the wavefunctions of electrons in atoms as well as molecules. Suppose that the function Wma = N(a)e* with N(a) the normalization constant and a an adjustable parameter, is used as a trial wavefunction for the 1s orbital of the hydrogen t atom. Show that 3ah? 2a - 2e E(a)=- where e is the fundamental charge, and µ is the reduced mass for the atom. What is the minimum energy associated with this trial wavefunction?Find the directions in space where the angular probability density for the l = 2, ml = 0 electron in hydrogen has its maxima and minima.
- Find the directions in space where the angular probability density for the l = 2, ml = 0 electron in hydrogen has its maxima and minima.In the subshell e = 3, (a) what is the greatest (most positive) me value, (b) how many states are available with the greatest mn, value, and (c) what is the total number of states in the subshell? (a) Number Units (b) Number Units (c) Number UnitsProve that the total degeneracy for an atomic hydrogen state having principal quantum number n is 2n2.
- A deuterium molecule (D2₂) at 30°K is known to be in the state, 1 /26 12/₂) = = |3|1, 1) + 4 |7, 3) + |7, 1) where , m) are eigenstates of the angular momentum operator. (a) If one were to measure L₂, what posible values one would get and what would be their associated probabilities? (b) Repeat (a) but for L². (c) What is the expectation value of the energy (E) of the molecule in this state, assuming purely rotational states. Take c= 30.4 cm-¹, where I=moment of inertia of D₂ and c=speed of light. Express your answer 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.Consider an electron in an external magnetic field in the SzS-direction, $\mathbf{B} B_z \hat{k}S. If the initial spin state of the electron is the eigenstate of SS_x$ with eigenvalue S+\hbar/2$, \begin{enumerate} \item[a)] Find the state of the system at time St$. \item [b)] Show that the system returns to its initial state and calculate the angular frequency. \item [c)] Calculates the expected value of SS_XS, SS_yS and SS_ZS as a function of time. \ end {enumerate}