Suppose a 1D quantum system is represented by the wavefunction in position space: (x|½(t)) = p(x, t) = Ae-3¤+5it where it only exists 0 < x <• ! Normalize the wavefunction, i.e., what is A?
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- Determine the normalization constant for the following wavefunction. Write an expression for the normalized wavefunction. (8) y=(r/ao)et/2a,Suppose that you have a 2D quantum system where X and Px are the x- component position and momentum operators and Y and Py are the y- component position and momentum operators. Which of the following commutators is not equal to 0? [Py,Y] O IX,Y] O [Px,Px] O [PxY]Evaluate the E expressions for both the Classical (continuous, involves integration) and the Quantum (discrete, involves summation) models for the energy density u, (v).
- A particle with mass m is in the state .2 mx +iat 2h Y(x,t) = Ae where A and a are positive real constants. Calculate the expectation values of (x).Suppose a 1D quantum system is represented by the wavefunction in position space: (æ]Þ(t)) = v(x, t) = Ae -3x+5it %3D where it only exists 0 < x <. What is (X)?