Recent content by physical_chemist

@PeterDonis, classically, when a particle is rotating about z-axis, the x,y components of angular momentum are zero, since L is a vector quantity and there is no rotation around such axes. But, in Quantum mechanics, there is an uncertainty relation which cannot allow this in principle (except...

As @DrClaude say, it is similar to the Bohr's procedure and confinement of an integer number of wavelengths on the circular trajectory of radius r. But, remember: this model is limited and based on classical concepts. It doesn't reflect the complete wave-like features of the electron confined by...

Yan, the Robertson uncertainty principle is regarding two operator have a common complete set of eigenfunctions, i.e., in such basis both operators are diagonal. This is usually expressed, for example, as $$\Delta A\Delta B \geq \frac{1}{2}\left | \int \psi^{*}[A,B]\psi d\tau\right |$$ But, in...

By considering a particle on a ring, the eigenfunctions of ##H## are also eigenfunctions of ##L_\text{z}##: $$\psi(\phi) = \frac{1}{\sqrt{2\pi}}e^{im\phi}$$ with ##m = 0,\pm 1,\pm 2,\cdots##. In polar coordinates, the corresponding operators are $$H =...