Laplace equation
sort by: Relevancy | Title try advanced search for more options
-
After showing how a double-minimum potential generates one-dimensional bonding, Professor McBride moves on to multi-dimensional wave functions. Solving Schrödinger's three-dimensional differential equation might have been daunting, but it was not, because the necessary formulas had been worked out more than a century earlier in connection with acoustics. Acoustical "Chladni" figures show how nodal patterns relate to frequencies. The analog...more
-
This lecture brings experiment to bear on the previous theoretical discussion of bonding by focusing on hybridization of the central atom in three XH3 molecules. Because independent electron pairs must not overlap, hybridization can be related to molecular structure by a simple equation. The "Umbrella Vibration" and the associated rehybridization of the central atom is used to illustrate how a competition between strong bonds and stable at...more
-
Government and Entrepreneurship: The Evolution of Entrepreneurship in China
Stanford / Entrepreneurship
Tarun Khanna, Professor at Harvard Business School, argues that the old equation that government = inefficient does not hold unilaterally but depends on the context. To illustrate, Khanna describes the evolution of the Communist Party of China and its efforts to co-opt entrepreneurs so that now the government and entrepreneurship is very closely integrated. In contrast, Khanna suggests that in India entrepreneurs keep their distance from t...more
-
After pointing out several discrepancies between electron difference density results and Lewis bonding theory, the course proceeds to quantum mechanics in search of a fundamental understanding of chemical bonding. The wave function ψ, which beginning students find confusing, was equally confusing to the physicists who created quantum mechanics. The Schrödinger equation reckons kinetic energy through the shape of ψ. When ψ curves toward zer...more
-
What a differential equation is and some terminology?
-
Figuring out the equation for the volume of a sphere.
-
Discriminative Algorithms, Generative Algorithms, Gaussian Discriminant Analysis (GDA), GDA and Logistic Regression, Naive Bayes, Laplace Smoothing
-
2 more examples of solving equations using the quadratic equation.
-
Laplace transform of e^at.
-
Solving a non-homogeneous differential equation using the Laplace Transform.
-
In this lecture, Professor Lewin displays how the conservation of mechanical energy can be used to derive the equation of motion for simple harmonic oscillators (SHO). In doing so he covers gravitational potential energy, equilibrium points where the net force is zero, parabolic potential energy, and circular potential energy.
-
This lecture is devoted to the electron diffraction experiment of 1927, where the wavelike nature of electron beams was experimentally established, thus supporting an underlying principle of quantum mechanics. Professor Sylvia Ceyer discusses how to calculate λ from θ, de Broglie wavelength, and concludes with Schrodinger's equation of motion for matter waves.
