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rlduncan
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Could some comment on conservative or nonconservative systems in the context of the hydrogen atom and the total energy E, as given in Schrodinger's equation.
Although not conserved separately, I am sure you realize.rlduncan said:It appears that a fundamental condition of Schrodinger's equation is that the total energy of the system remains constant. This then implies that the kinetic energy and potential energy must be constant, a conservative system.
Where does this equation come from? It's not a wave equation in the usual sense (unless you mean that x is a time variable). It certainly doesn't have anything to do with a hydrogen atom. Or am I misinterpreting and is supposed to be the wavefunction? (If so, it's not a regular solution to the hydrogen atom.)In the wave equation y=Asin(kx), k is constant and is not a function of the x variable (lets assume one dimension).
However, k=2*pi/lambda and if lambda is the debroglie wave and varies as a function of x, how is it possible to take a simple derivative as if k is a constant. Also for the h-atom the total energy varies with the kinetic energy and potential energy, a nonconservative system.
rlduncan said:Could some comment on conservative or nonconservative systems in the context of the hydrogen atom and the total energy E, as given in Schrodinger's equation.
rlduncan said:Looking at the total energies of the hydrogen atom as given buy Bohr's equation which I assume are valid. For example, for n=1:KE=13.6, PE=-27.2, and E, the total energy sums to -13.6ev. For n=2:KE=3.4, PE=-6.8, and E=-3.4ev. The sum of the initial KE and PE does not equal the sum of the final KE and PE which I assume should be the same for a conservative system.
rlduncan said:I agree, but this seems to suggest a nonconservative system.
rlduncan said:I agree and that is my point. In Schrodinger's equation the total energy is the sum of KE and PE and when solved the total energy is assumed to to be a constant. The KE =E-V(r). However, according to Bohr equations it is not mathematically a constant unless you included the photon energy.
rlduncan said:It appears that a fundamental condition of Schrodinger's equation is that the total energy of the system remains constant. This then implies that the kinetic energy and potential energy must be constant, a conservative system. In the wave equation y=Asin(kx), k is constant and is not a function of the x variable (lets assume one dimension). However, k=2*pi/lambda and if lambda is the debroglie wave and varies as a function of x, how is it possible to take a simple derivative as if k is a constant. Also for the h-atom the total energy varies with the kinetic energy and potential energy, a nonconservative system.
A conservative system is a physical system where the total energy remains constant over time. This means that energy cannot be created or destroyed within the system, it can only be transferred between different forms.
The hydrogen atom is the simplest and most abundant element in the universe. It consists of a single proton in the nucleus and a single electron orbiting around it.
Schrodinger's equation is a mathematical equation used to describe the behavior of quantum mechanical systems, including conservative systems such as the hydrogen atom. It allows scientists to calculate the energy levels and probability distribution of an electron in the hydrogen atom.
In the hydrogen atom, energy plays a crucial role in determining the behavior and stability of the electron. Schrodinger's equation is used to calculate the energy levels of the electron in different orbitals, which ultimately determine the chemical properties of hydrogen.
Yes, Schrodinger's equation can be applied to any conservative system, as long as the system can be described by quantum mechanics. This includes other atoms and molecules, as well as larger systems such as crystals and solids.