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.

An ambulance emits a frequency of 450 hz from its siren. what frequency is heard by a man as the ambulance moves toward him? less than 450 hz more than 450 hz 450 hz 0 hz

Which statement is true for light passing into a medium that is more optically dense than the first medium through which it past

Consider the particle-in-a-box problem in 1d. a particle with mass m is confined to move freely between two hard walls situated at x = 0 and x = l. the potential energy function is given as (a) describe the boundary conditions that must be satisfied by the wavefunctions ψ(x) (such as energy eigenfunctions). (b) solve the schr¨odinger’s equation and by using the boundary conditions of part (a) find all energy eigenfunctions, ψn(x), and the corresponding energies, en. (c) what are the allowed values of the quantum number n above? how did you decide on that? (d) what is the de broglie wavelength for the ground state? (e) sketch a plot of the lowest 3 levels’ wavefunctions (ψn(x) vs x). don’t forget to mark the positions of the walls on the graphs. (f) in a transition between the energy levels above, which transition produces the longest wavelength λ for the emitted photon? what is the corresponding wavele