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[math code]

The Hamiltonian of a free particle is \[ H = {1\over 2m} \sum^3_{i-1} p^2_i.\label{2solp1e1}\]

The Heisenberg equations of motion for \(p_i\) and \(x_j\) are \[{dp_j\over dt} = {1\over i\hbar} [p_j, H] = 0,\label{2solp1e2}\] \[ {dx_j\over dt} = {1\over i\hbar}[x_j, H] = {1\over 2i\hbar m}\sum^3_{i=1}[x_j, p^2_j] = {p_i\over m},\label{2solp1e3}\]

From Eq. {2solp1e2} we have \(p_j(t) - p_j(0)\).

Hence the solution of Eq.{2solp1e2} is \[ x_j(t) = x_j(0) + {p_j(0)\over m}t.\label{2solp1e4}\]

Since \([x_i, p_j] = i\hbar\delta_{ij}\) we obtain \[ [x_j(t), x_i(0)] = -{i\hbar t\over m}\delta_{ij}.\label{2solp1e5}\] \setcounter{equation}{0}

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            class ComplexNumber:
    def __init__(self, r=0, i=0):
        self.real = r
        self.imag = i

    def get_data(self):
        print(f'{self.real}+{self.imag}j')


# Create a new ComplexNumber object
num1 = ComplexNumber(2, 3)

# Call get_data() method
# Output: 2+3j
num1.get_data()

# Create another ComplexNumber object
# and create a new attribute 'attr'
num2 = ComplexNumber(5)
num2.attr = 10

# Output: (5, 0, 10)
print((num2.real, num2.imag, num2.attr))

# but c1 object doesn't have attribute 'attr'
# AttributeError: 'ComplexNumber' object has no attribute 'attr'
print(num1.attr)
        

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