Stern Gerlach Experiment

Stern - Gerlach Expenment.- ANeutral Beam of silver atoms in ground state is splitted into two beams on passing though in homoheneous magnetic field There are no clear mathematical equations or formulas. The content seems to be a collection of random characters and abbreviations without a clear context or meaning. Consider that the velocity of atoms in Beam along the direction of propagation of beam is ve, i atoms present in magnetic field region for t. length of the magnetic L. (mass of each atom is m) Uz = 0, acceleration → Az MsZ = -2eSz Uz = 0 Z = Uzt + azt^2 / 2 = -2eSz / 2m = -2mSB There are also numbers and symbols like +, -, =, and arrows. The equations are arranged in multiple lines without clear structure or alignment. The handwriting is neat in some parts but difficult to read in others, especially for some symbols. The equations involve variables such as az, Coso, Z, MB, JB, and 14>. There are also numbers and symbols like +, -, =, and arrows. The equations are arranged in multiple lines without clear structure or alignment. The handwriting is neat in some parts but difficult to read in others, especially for some symbols. The text is simple and consists of three words: "Onoy," "to," and "option-c." The words are aligned horizontally. The content includes mathematical equations, references to eigenstates and eigenvalues, and some unclear symbols. The text is arranged in multiple lines with inconsistent spacing. There is no clear structure or pattern in the arrangement of the text. let 1Ψ be an eigenstate of I with eigen Value A۰ H^│Ψ 2> = x²/4> he equations involve variables such as λ, 14>, 13>, 121², 2.7², and 1221£147. There are also numbers and symbols like +, -, =, and arrows. The equations are arranged in multiple lines without clear structure or alignment. The handwriting is neat in some parts but difficult to read in others, especially for some symbols. Below the equations, there is the text "(option-d)," followed by "Ques.l.," "เล," and "lel I = Y." The radial distance r is expressed in Cartesian coordinates as the square root of the sum of the squares of x, y, and z. The handwriting is neat and legible. for spin-1/2 H = Eσ(σx + ασy) let |4> be eigen state of H with eigen value. ⇒ λ² = E₀²(1 + α²) H|4> = λ|4> H²|4> = λ²|4> = E₀²(1 + α²)|4> λ = ±E₀√(1 + α²) (option-a) For a spin-1/2 particle show that e^(iθσ̂n) = cosθ + i(σ̂ · n) sinθ where n̂ is unit vector along arbitrary dirn. θ is a particular angle., σ̂ is Pauli's spin operator. The equations are not well-formed and appear to be fragments of larger calculations. There is no clear structure or pattern to the equations, and they are scattered across the image. The handwriting is somewhat messy and difficult to read in some places. The content appears to be related to quantum mechanics, specifically the derivation or representation of the exponential of a Pauli spin operator. The handwriting is neat and legible. e^(iθσ̂n) = cosθI + i sinθ σ̂n Prob. For a spin - particle show that (.Ả) (7.8) = AB+ lỡ. (ẢXB) Where σ is pauli's spin operator À & B are vectors in position space other than spin σ = (σx i + σy j + σz k) (σA) = (σx Ax + σy Ay + σz Az) (σB) = (σx Bx + σy By + σz Bz) (σA)(σB) = (σx Ax + σy Ay + σz Az)(σx Bx + σy By + σz Bz) (σA)(σB) = (σxAx + σyAy + σzAz)(σxBx + σyBy + σzBz) = σxAxσx Bx + σxAxσyBy + σxAxσzBz + σyAyσx Bx + σyAyσyBy + σyAyσzBz + σzAzσx Bx + σzAzσyBy + σzAzσzBz = i²AxBy + i²AyBx + σxσy(AxBy + AyBx) + i²AzBx + i²AyBz + σyσz(AyBz + AzBy) + i²AxBy + i²AzAy + σzσx(AzBx + AxBz) = i²(AxBy + AyBx + AzBx + AyBz + AxBy + AzAy) + σxσy(AxBy + AyBx) + σyσz(AyBz + AzBy) + σzσx(AzBx + AxBz) = i²(2AxBy + 2AyBx + 2AzBz) + σxσy(AxBy + AyBx) + σyσz(AyBz + AzBy) + σzσx(AzBx + AxBz) = 2i²(AxBy + AyBx + AzBz) + i(σxσy + σyσx)(AxBy + AyBx) + i(σyσz + σzσy)(AyBz + AzBy) + i(σzσx + σxσz)(AzBx + AxBz) = 2i²(AxBy + AyBx + AzBz) + 2i(σxσy)(AxBy + AyBx) + 2i(σyσz)(AyBz + AzBy) + 2i(σzσx)(AzBx + AxBz) = 2i(i(AxBy + AyBx + AzBz) + σxσy(AxBy + AyBx) + σyσz(AyBz + AzBy) + σzσx(AzBx + AxBz)) = 2i(iAB + (σxσy + σyσx)Axy + (σyσz + σzσy)Ayz + (σzσx + σxσz)Azx) = 2i(iAB + 2iεxyz Axy + 2iεyzx Ayz + 2iεzxy Azx) = 2i(iAB + 2iεijk Ajk) = 2i²(AB + εijk Ajk) = -2(AB - εijk Ajk) = AB + iεijk Ajk Ax Ay Az Bx By Bz Cx Cy Cz J. (AxB) = σx σy σz Ax Ay Az Bx By Bz Cx Cy Cz