The Hamiltonian Operator is the operator for the total energy of a conserved system. A conserved system experiences no loss due to dissipative forces such as friction, wind resistance, etc.
Total Energy = Kinetic Energy + Potential Energy
We can employ this equation for a point source mass that is a child at the top of a slide. There, the point mass has no kinetic energy and all of the total energy is potential energy. At the moment the point mass reaches the bottom of the slide there is no potential energy and all the total energy is kinetic energy. At points on the slide between the top and the bottom the total energy is a sum of potential energy and kinetic energy.
Of course, for this “cartoon” scenario to be true, there would have to be no wind resistance and the slide would have to be made out of a “frictionless” material (what rule or idea of chemistry makes it impossible for a material to be frictionless?)
This example is analogous an object sliding down an inclined plane and that problem is (in our opinion) one of the top five exercises that an undergraduate physicist can do!
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A prayer: “Oh Michael, Oh Jesus, how much time has been lost because it isn’t obvious that T goes to Kinetic Energy and V goes to Potential Energy?”
The song “Turn that Heartbeat Over Again” is on an album by Steely Dan, released in 1972.
Rob Sterling 