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Q: b) Find the commutator relation 1) [Z², L,] 2) [H,x]
A: (1) [ z2, Lz] = [zz,Lz] = z[z,Lz] + [z,Lz]z But, [z,Lz] = 0 then,…
Q: (a) (b) (c) 1. Consider a system with two spin ½ particles in a four-dimensional basis |s₁m₁₂m₂ >: 1…
A: The objective of the question is to find the matrix representations of the spin operators S1z, S2z,…
Q: For 3-dimensional rotational motion of an electron, the generalized wavefunction is: eimio · Olm, ,…
A: For the 3-dimensional rotational motion of an electron the generalized wavefunction is; ψ =12π eimlϕ…
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Q: Taking into account electron spin, what is the total number of states with n=3?
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A: v = 9.11/cos 56.8°
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Q: You have 3 spin-1/2 particles in the following state: |ψ⟩ = 1/√2 (|+z⟩1 |+z⟩2 |+z⟩3 + |-z⟩1 |-z⟩2…
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Q: View a system of two particles that do not interact with each other, where each particle can occupy…
A: The partition function is given by z=Σgie-βE β=1/(kBT) kB =Boltzman constant
Q: 7) Find the torgue exparoced Dy a moyuwtie dijade with Monut(ir 32AwR). in a mguetir feld (î- 0.25
A: Given, magnetic momentμ⇀ = 32 A-m2 x⏞ magnetic field B⇀ = 0.25 T z⏞
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A: Given energy equation is denoted as, E(α)=3αh22μ-2e2(2απ)1/2 To find the minimum energy given below.
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Q: What is the graph of its derivative, h'?
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- Show that the total Coulomb self-energy of a sphere of radius R containing a charge Ze evenly spread throughout the sphere is given by as attached.Recall for an the hydrogenic (single electron) atom 2s (r) = 2,0,0 (r, 0, 4) Φ2p (r) = Φ2,1,0 (r,θ, φ) - = 2p (7) = 2p_ (F) = 2,1,1 (r, 0, 6): = 2,1,-1 (r, 0,6) 1 4√2π/² p 1 3/2 ao 4√/2πа = 2 δεν παρ Tº 3/2 ao 8√πа 3/2 ao 1) e-r/2² ao e ○ (02s (71)2p, (72) + O2p. (71)02s (72)) O 02s (1) 2po (2) ○(28 (71)2p, (72) – $2p. (71)¢2s (72)) O 02s (1)02s (F2) T -T 12a0 •/200 cos 0, /2ao sin 0 etic. r/2ao sin 0 e-iç Consider the helium atom (two electron system). Suppose the spin part is one of the triplet. Which of the following can be a possible space part?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.
- #8Calculate the number of angles that L can make with the z-axis for an l=3 electron.There exists in nature a particle known as the muon. It is just a heavy electron with a mass mµ = 207me. It decaysin 10−6seconds. Suppose there exists a molecule analogous to H+2(two protons + 1 electron), but with the electronreplaced by a muon:(a) Find the equilibrium separation of the nuclei (R0) in such a molecule.(b) If a rotational state is excited, estimate the wavelength of the emitted radiation in the transition to the groundstate
- We have a three dimensional vector space where |P1), |P2) and |23) form a complete orthonormal basis. In this vector space we have two states |a)=5i|1)+3i 2)+(-2+2i) 3) and |B) =4i|1)-5 i) Calculate (a and (B, in terms of the dual basis vectors (y|, (p2|, (P3|. ii) Calculate the inner/scalar products (alB) and (Ba). Show that (8|a) =(a|B)".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}