Calculate the energy of the five non interacting spin particles in a three-dimensional box of length L. (15)z²h? (a) 2mL? (25)z’h? (b) 2mL (24)z’n² (c) 2mL? (30)r’h (d) 2mL?
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Calculate the energy of the five non interacting spin 1/2 particles in a three dimensional box of length L.
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- Electrons in a hydrogen atom are in a 3p excitation state transitioning radiative to energy level 2s. Taking into account the spin orbital interaction, determine : i) What is a spin orbit interaction?ii) Show the separation of 3p and 2s energy levels in the energy level diagramwithout an external magnetic field Biii) Show the separation of 3p and 2s energy levels in the energy level diagram due to the presence of an external magnetic field Biv) State the allowed transition conditionsv) Energy emitted when in space without a magnetic fieldvi) Energy emitted if it is in a space with a magnetic field B = 1Tplease solve part iA hydrogen atom is located in an area where there is both a uniform magnetic field and a uniform electric field that are parallel to each other. a) write out the Hamiltonian of perturbation (ignore the spin of the electron). b) use perturbation theory in order to calculate the first order correction to the energy levels n=1,2 c) is there any degeneracy left? Compare with situations in which there is a magnetic field or only an electric field.A spin-particle is in the spin state |A), described by the ket 7 i |4) = 5√2 tu) +5√2 tu). (a) Verify that A) is normalised. (b) Using the spinor representation (+₂) = ₁ | +) = √/2₁ 11³) = ₁ 1 +2) = [8] find the values of c₁ and c₂ for which |A) = C₁|1₂) + C₂l+₂). (c) If the observable S₂ is measured in the spin state |A), what values can be obtained and what are their probabilities? (d) Find the expectation value of S₂ in the spin state [A). (e) With reference to the properties of angular momentum, explain briefly how the results of the Stern-Gerlach experiment provide evidence of the existence of spin.
- Suppose you measure the angular momentum in the z-direction L, for an /= 2 hydrogen atom in the state | > 2 > |0 > +i/ |2 >. The eigenvalues of %3D V10 10 Lz are – 2h, -ħ, 0, ħ, 2ħfor the eigenvectors | – 2 >, |– 1>, |0 >, |1 >, |2 >, respectively. What is AL,? V31 10 7 19 25Rewrite S₁ S₂ in terms of S², |S₁|², 5₂|² by using the identity |S² = |S₁ + S₂|² = |S₁|² + |5₂|² +25₁ · 5₂. Use this to show that the combined spin angular momentum basis 5² for the electron and proton spins is an eigenstate basis for this dipole interaction.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}