Question

For the electron in the hydrogen atom, which of the sets of observables below are compatible observables?

a) No compatible observables exist. The uncertainty principle prevents us from knowing the value of two observables simultaneously.
b) The total energy, the magnitude of the orbital angular momentum, and its component along the z-axis.
c) The momentum, the magnitude of the orbital angular momentum, and its component along the z-axis.
d) The x, y, and z components of the orbital angular momentum.
e) The position, the total energy, and the magnitude of the orbital angular momentum.

Answer 1

The compatible observables for the electron in the hydrogen atom are the total energy, magnitude of the orbital angular momentum, and its component along the z-axis.

option a is the correct

Step-by-step explanation:

The compatible observables are:

• The total energy
• The magnitude of the orbital angular momentum
• The component along the z-axis

These observables are compatible because they can all be measured simultaneously with precision. The Heisenberg uncertainty principle does not prevent us from knowing the values of these observables at the same time.