Observables and operators
Operators momentum, Hamiltonian, and Energy
1. In an experiment, the quantity x is measured. Ten consecutive measurements give the following values: 4, 7, 6.5, 8, 5, 8, 6, 7.5, 9, and 7. Calculate the average value and the uncertanty.
2. Calculate the expectation and the uncertainty in a “throw of the die” experiment. (i.e., six values from 1 to 6 with equal probability).
3. In an experiment, the probability of measuring the quantity x is given by the distribution P(x)=Aexp(x) for x<0 and P(x)=Aexp(-x) for x>0 . Calculate the value of A that normalizes the distribution. Calculate the expectation of x and its uncertainty Dx..
4. The result of an experiment has the same probability of giving any (continuous) value between 1 and 6, while there is 0 probability of giving any other value. Calculate the expectation of x and the uncertainty Dx.
5. Calculate modulus and phase for the following complex numbers:
a) 10 + i 7
b) -8 + i 16
c) 4 - i 12
6. Calculate real part and imaginary part for the complex number
the following modulus an phase:
modulus phase (in radians)
a) 24 p
b) 12 5
c) 1 1
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