2 methods for solving first order odes
... where K = eC is an arbitrary positive constant. Solving for y we obtain y = ±Ke3x . Noting that ±K is an arbitrary non-zero constant, we relabel it as K, dropping the condition that K be positive, or y = Ke3x . We can see by simply plugging into the DE that the constant function y = 0 also solves th ...
... where K = eC is an arbitrary positive constant. Solving for y we obtain y = ±Ke3x . Noting that ±K is an arbitrary non-zero constant, we relabel it as K, dropping the condition that K be positive, or y = Ke3x . We can see by simply plugging into the DE that the constant function y = 0 also solves th ...
lecture 2
... • waves are collective bulk disturbances, whereby the motion at one position is a delayed response to the motion at neighbouring points • propagation is defined by differential equations, determined by the physics of the system, relating derivatives with respect to time and position ...
... • waves are collective bulk disturbances, whereby the motion at one position is a delayed response to the motion at neighbouring points • propagation is defined by differential equations, determined by the physics of the system, relating derivatives with respect to time and position ...
powerpoint
... The rotation operator represents a geometrical action that preserves the normalization, and therefore 1 = || 2 (Unitary Operator) The angular momentum operator represents a measurable physical quantity, and therefore all the eigenvalues are real (Hermitian Operator) ...
... The rotation operator represents a geometrical action that preserves the normalization, and therefore 1 = || 2 (Unitary Operator) The angular momentum operator represents a measurable physical quantity, and therefore all the eigenvalues are real (Hermitian Operator) ...
Lesson 1 Parallel and Perpendicular Lines
... a. The lines are perpendicular since their slopes are negative reciprocals. b. Write the second equation in slope-intercept form to find the slope. 8x + 2y = 12 y = -4x + 6 The lines are parallel since they have the same slope, m = -4. c. Write the second equation in slope-intercept form. 6x - 9y = ...
... a. The lines are perpendicular since their slopes are negative reciprocals. b. Write the second equation in slope-intercept form to find the slope. 8x + 2y = 12 y = -4x + 6 The lines are parallel since they have the same slope, m = -4. c. Write the second equation in slope-intercept form. 6x - 9y = ...
Problems in Quantum Mechanics
... called the density matrix , and show that the expectation value of the observable associated with operator  in |ψi is tr{ρ̂Â}. 4.2 Statistical mechanics Frequently physicists don’t know exactly which quantum state their system is in. (For example, silver atoms coming out of an oven are in states ...
... called the density matrix , and show that the expectation value of the observable associated with operator  in |ψi is tr{ρ̂Â}. 4.2 Statistical mechanics Frequently physicists don’t know exactly which quantum state their system is in. (For example, silver atoms coming out of an oven are in states ...
