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Buck_minster
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If the electron of the h-atom is not moving in a classical orbit (like a circular orbit) why is the reduced mass used in Schrodinger's equation?
The use of the electron reduced mass in the electronic schrödinger equations for H+2
Abstract
It is shown that for H+2 and its isotopes, the electronic Schrödinger equation involving the electron rest mass me can be related in a simple way to that involving the electron reduced mass μe = me(ma + mb)/(me + ma + mb) by a straight-forward scaling of all distances in the first of these equations by μe/me. A numerical comparison of the two approaches is made at the adiabatic level of approximation for HD+, and it is seen that any differences would have only a negligible effect on the calculated vibration-rotation spectrum.
granpa said:I don't know but have you seen this
Actually not. Consider two masses, m and M, connected by a linear spring with a spring constant k. Assuming no angular momentum and no damping, so that the motion is only axial, what is the natural resonance frequency ω0 of this linear harmonic oscillator? It should be (I am guessing)Buck_minster said:It appears that the reduced mass is necessary in predicting hydrogen's electronic states, but what about the angular momentum of the ground state of the H-atom? Doesn't this type of motion being discussed imply nonzero angular momentum?
The reduced mass is used in Schrodinger's equation to account for the relative motion of two particles in a system. It allows for a more accurate calculation of the system's energy levels and wavefunctions.
To calculate the reduced mass, you first need to know the masses of the two particles in the system. Then, you can use the formula μ = m1m2 / (m1 + m2), where μ is the reduced mass, m1 is the mass of one particle, and m2 is the mass of the other particle.
The reduced mass is important in quantum mechanics because it is used to determine the energy levels and wavefunctions of a system. These values are crucial in understanding the behavior and properties of particles in a quantum system.
The reduced mass has a direct impact on the energy levels of a system. As the reduced mass increases, the energy levels become closer together, resulting in a more tightly bound system. On the other hand, a smaller reduced mass leads to wider energy level spacing and a less tightly bound system.
No, the reduced mass cannot be negative. It is a mathematical quantity that is derived from the masses of the particles in a system, which are always positive values. Therefore, the reduced mass will also always be a positive value.