Schrodinger’s equation predicts that the total energy of a particle trapped in a potential well is quantized and comes in discrete values in other words the energy distribution is not continuous as shown in Figure 4 below. $$E=\frac\) and express \(ℏ\) in terms of Plank’s constant we get Stack Exchange network consists of 183 Q&A communities including Stack Overflow. For a nonrelativistic (moving at speeds much less than the speed of light), massive particle that is an isolated system the total energy of the particle is just its kinetic energy: The Schrodinger equation plays the role of Newtons laws and conservation of energy in classical mechanics - i.e., it predicts the future behavior of a dynamic system. I reviewed part of my notes in the quantum mechanics class, and still have a few questions about the variational derivation of the Schrodingers equation: The variational principle says that the. K + V E We then multiply both sides by and assume it has the wave form ei ( kx t). Recall energy conservation, where the total energy E is the sum of kinetic K and potential energy V. The eigenvalues \(E_i\) of the energy operator are the possible measurable values of the total energy of a quantum system. An explanation for the motivation of Schrödingers that I have heard is similar and is an extension of your own.
