1. The problem statement, all variables and given/known data
These are rather simple questions but the rules for all of this are not quite clear to me yet. I'm to determine whether or not the following states are "legal" and if not I should normalize them.
a. ##\frac{1}{√385} ∑_{x=1}^{10}x^2 |x>##
b. ##\frac{1}{√2} |u_x>+\frac{1}{√2} |u_z>##
c.##e^{0.32i}(0.01|0>+0.25|1>+0.16|2>##
2. Relevant equations
3. The attempt at a solution
For a I believe I am correct in in simply squaring the fraction and the sum giving me a number much greater than 1 (≈385). So, in that case, the normalization factor 'N' would just be ##\frac{1}{385}## in order to make it 1.
For b my lack of understanding is obvious. At first glance I can see that the equation is normalized but the bases are not the same. In class we switch bases in this case but I don't know if I can say the equation is normalized as it is. Is this a legal description of the state that I can say is normalized or is it necessary to switch to common bases and introduce a normalization factor?
Lastly c, I believe is fine as it is. However, I just want to get confirmation on what the exponential actually is. So far in class we have ignored exponentials and the complex 'i'. Are these just some sort of phase constants?
These are rather simple questions but the rules for all of this are not quite clear to me yet. I'm to determine whether or not the following states are "legal" and if not I should normalize them.
a. ##\frac{1}{√385} ∑_{x=1}^{10}x^2 |x>##
b. ##\frac{1}{√2} |u_x>+\frac{1}{√2} |u_z>##
c.##e^{0.32i}(0.01|0>+0.25|1>+0.16|2>##
2. Relevant equations
3. The attempt at a solution
For a I believe I am correct in in simply squaring the fraction and the sum giving me a number much greater than 1 (≈385). So, in that case, the normalization factor 'N' would just be ##\frac{1}{385}## in order to make it 1.
For b my lack of understanding is obvious. At first glance I can see that the equation is normalized but the bases are not the same. In class we switch bases in this case but I don't know if I can say the equation is normalized as it is. Is this a legal description of the state that I can say is normalized or is it necessary to switch to common bases and introduce a normalization factor?
Lastly c, I believe is fine as it is. However, I just want to get confirmation on what the exponential actually is. So far in class we have ignored exponentials and the complex 'i'. Are these just some sort of phase constants?
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