Quantum Mechanics
... b. Determine the complete set of states, the corresponding energy spectrum and orthonormalize the stationary states. c. Assume now that the particle has charge q and is placed in a small electric field ~ = Eêx . Determine the first non-zero perturbative correction to the energy levels. ...
... b. Determine the complete set of states, the corresponding energy spectrum and orthonormalize the stationary states. c. Assume now that the particle has charge q and is placed in a small electric field ~ = Eêx . Determine the first non-zero perturbative correction to the energy levels. ...
MIT Physics Graduate General Exams
... Students studying for the Fall 2003 Part I exam found it useful to first categorize each problem by the concept they thought was being tested. Such an approach simplified their subsequent attempt at solving the problem. The following is a list of all the concepts they thought could be used as the ba ...
... Students studying for the Fall 2003 Part I exam found it useful to first categorize each problem by the concept they thought was being tested. Such an approach simplified their subsequent attempt at solving the problem. The following is a list of all the concepts they thought could be used as the ba ...
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
... 16. State and prove Ehernfest’s theorem 17. Solve the Schrodinger equation for a linear harmonic oscillator. Sketch the first two eigenfunctions of the system. 18. Determine the eigenvalue spectrum of angular momentum operators Jz and Jz 19. What are symmetric and antisymmetric wave functions? Show ...
... 16. State and prove Ehernfest’s theorem 17. Solve the Schrodinger equation for a linear harmonic oscillator. Sketch the first two eigenfunctions of the system. 18. Determine the eigenvalue spectrum of angular momentum operators Jz and Jz 19. What are symmetric and antisymmetric wave functions? Show ...
Noether's theorem
Noether's (first) theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law. The theorem was proven by German mathematician Emmy Noether in 1915 and published in 1918. The action of a physical system is the integral over time of a Lagrangian function (which may or may not be an integral over space of a Lagrangian density function), from which the system's behavior can be determined by the principle of least action.Noether's theorem has become a fundamental tool of modern theoretical physics and the calculus of variations. A generalization of the seminal formulations on constants of motion in Lagrangian and Hamiltonian mechanics (developed in 1788 and 1833, respectively), it does not apply to systems that cannot be modeled with a Lagrangian alone (e.g. systems with a Rayleigh dissipation function). In particular, dissipative systems with continuous symmetries need not have a corresponding conservation law.