9. Considering that spin state of a particle is known in the rest system of this particle, find bispinor u(p) in coordinate system, where the particle has momentum p. Using this result find connection between average values of spin vector of the particle in mentioned above coordinate systems. 10. Show that for Dirac particle with mass m-0 the operator ys commutes with Hamiltonian of the free particle. Find eigenvalues of this operator and explain their physical meaning.

9. Considering that spin state of a particle is known in the rest system of this particle, find bispinor u(p) in coordinate system, where the particle has momentum p. Using this result find connection between average values of spin vector of the particle in mentioned above coordinate systems. 10. Show that for Dirac particle with mass m-0 the operator ys commutes with Hamiltonian of the free particle. Find eigenvalues of this operator and explain their physical meaning.

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Consider the following statements about the Hartree-Fock method and decipher if they are True (T), False (F) or indeterminable (i.e. more information is needed) The wavefunction consists of a single Slater determinant → this is (T, For l) It includes the exchange energy approximately → this is (T, For l) It includes exchange which only occurs between electrons of opposite spin → this is (T, For l) Due to the electron-electron interactions the computer time scales as a function of the number of basis functions to the power of 4 → this is (T, For l) A spin-polarized calculation on a material with an odd number of electrons will result in spin orbitals that have the same energy and spatial wavefunction. → this is (T, F or l) A single determinant wavefunction is a correlated wavefunction. → this is (T, F or l) The two-electron contributions to the energy for a pair of electrons with opposite spin is equal to (Jij). → this is (T, F or l)
Chemistry.
1. Show that wavefunctions in particle in a box are orthonormal
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1) The following questions concern commutation relations, by applying it to an arbitrary function.
In your own words, briefly explain why the nodes in the particle-in-a-box wavefunctions ensure that the wavefunctions are orthogonal. You answer should include the meaning of orthogonal.
If the operator A acts on the orthonormalized real functions f, and f₂ as Af₁ = f₂ and Âf₂ = f₁. The expectation value of A for the state W=7f₁ + 21f₂ is a. 147.0 b. 490.0 c. 28.0 d. 73.5 e. 294.0
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