After completing an introduction to quantum mechanics course, i am concerned that i do not fully understand what a 'fuzzy' observable is in quantum mechanics, although it has been mentioned significantly in my course. could someone explain what this means in as much detail as possible? i am realizing that while i have a strong grasp of the mathematics, i sometimes overlook the basic physical meaning on things which can lead to me arriving at correct answers, but still not completely understanding what i just did. fuzzy observables seem to be another one of these situations.

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

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