Can the angular momentum and kinetic energy of a particle be measured simultaneously to arbitrary precision?
4.21. Show that the angular momentum and kinetic energy operators commute and therefore can be measured simultaneously to arbitrary precision.
Does position commute with angular momentum?
The operator nature of the components promise difficulty, because unlike their classical analogs which are scalars, the angular momentum operators do not commute. Example 9–1: Show the components of angular momentum in position space do not commute.
How many allowed values of the z component of the angular momentum are there?
three values
Lz can have three values, given by Lz=m1h2π L z = m 1 h 2 π . Thus, θ1 = cos−1 0.707 = 45.0º.
Why can we not know the position and momentum of an electron at any given moment?
Gamma rays are really high energy (short wavelength – that is how the “see” an electron). Since you can only “see” electrons with super high energy light, the “seeing” process actually changes the momentum of the electron and sends it flying. So you can’t know both position and momentum with accuracy.
Why position and momentum Cannot be precisely determined?
Originally Answered: Why can’t you measure the position and the momentum at the same time in quantum mechanics? Because a particle just does not have both an exact position and exact momentum. It can have one or the other or a combination of both.
What happens if you try to measure the position of an electron?
It is therefore impossible to follow an electron in its orbit around an atom. If you measure the electron’s position, you will find it in a definite location, but the atom will be disrupted.
Does angular momentum and work have same dimensions?
In option b) we have angular momentum and work. Now for angular momentum, the SI unit is kilogram metres square per second that is kg⋅m2⋅s−1. In the dimensional formula it can be written as ML2T−1. Therefore, the pair b) does not have the same dimensions.