By: Maria Christine L. Lugo, MS Physics I, MSU-IIT Show that a.) b.) Solution: a.) We can expand by its components and S_{2}^{2}, But we know that, (See link https://www.quantumsciencephilippines.com/?p=5698 ) Therefore, b.) Using the eigenvalue equation of and substituting the basis We have, […]
Archive for May 21st, 2019
Matrix representation of the square of the spin angular momentum
Tuesday, May 21st, 2019Posted in Eigenvalues And Eigenvectors, Linear Vector Space, Quantum Physics, Quantum Science Philippines | No Comments »
Orthogonality of Two Eigenvectors
Tuesday, May 21st, 2019Orthogonality of Two Eigenvectors by: Mariel A. Escobal, MS Physics I, MSU-IIT Prove that two eigenvectors of a Hermitian operator corresponding to two different eigenvalues are orthogonal. Consider two eigenvectors |ψ⟩ and |φ⟩ of the Hermitian operator Â, Â|ψ⟩ = λ|ψ⟩ (1) Â|φ⟩ = μ|φ⟩ (2) Since  is Hermitian, we can write (2) as ⟨φ| = μ⟨φ| (3) Multiplying […]
Posted in Eigenvalues And Eigenvectors, Hermitian Operators, Quantum Physics, Quantum Science Philippines | No Comments »
Eigenvalues of Hermitian Operators
Tuesday, May 21st, 2019Prove that the eigenvalues of a Hermitian operator are real. by: Mariel A. Escobal, MS Physics I, MSU-IIT Let Ĥ be a Hermitian operator on an inner product space V over the field of complex numbers . That is Ĥ = Ĥ+. Then, for an eigenvector |φ⟩ ∈ V, |φ⟩ ≠ |0⟩, and eigenvalue λ ∈ . Ĥ |φ⟩ = λ |φ⟩ We know for a general operator  on […]
Posted in Eigenvalues And Eigenvectors, Hermitian Operators, Quantum Physics, Quantum Science Philippines | No Comments »
Properties of Operator
Tuesday, May 21st, 2019Properties of Operators by: Mariel A. Escobal, MS Physics I, MSU-IIT Show the following where A & B are operators: a. (A+)+= A b. (λA)+=λ*A+ c. (A + B)+= A+ + B+ d. (AB)+= B+ A+ Solutions: a. (A+)+= A The adjoint of an operator is defined as: ⟨ψ|Aφ⟩=⟨A+ψ|φ⟩ Now, taking the complex conjugate of […]
Posted in Hermitian Operators, Quantum Physics, Quantum Science Philippines | No Comments »
Derive Bhor’s quantization condition from De Broglie’s relation.
Tuesday, May 21st, 2019by Jomari L. Tanghal, MS Physics I, MSU-IIT Derive Bhor’s quantization condition from De Broglie’s relation. Solution: Assume that an integral number of wavelengths must fit in the circumference of an orbit. The circumference of the circular orbit must be an integral of wavelength given by, from De Broglie’s wavelength, . This […]
Posted in Quantum Science Philippines | No Comments »