- #1
Kenneth Adam Miller
- 20
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Hello, I'm a beginner at quantum mechanics. I'm working through problems of the textbook A Modern Approach to Quantum Mechanics without a professor since I am not going to college right now, so I need a brief bit of help on problem 1.10. Everything else I have gotten right so far, but I am having trouble understanding how to apply the examples provided in order to attain an observation probability that does not have an imaginary component.
To explain, the state:
##|phi> = 1/2 * | +z > + i*sqrt(3)/2 * | -z >##
And we wish to know ##<S_x>##, where ##|+x > = 1/sqrt(2)*|+z> + 1/sqrt(2)*|-z>##
Since there is not an imaginary component for |+x>, I don't see how I can calculate ##<+x | phi >##; there is not an i to negate for ##|+x>## to acquire the complex conjugate <+x|. Perhaps I don't understand the complex conjugation part well enough - equal magnitude and opposite sign, yes?
So, then when I'm calculating ##<+x | phi >## according to the example, I wind up with an expectation value with an imaginary component. Which I don't think is correct.
Can anybody help point out where I have gone wrong?
To explain, the state:
##|phi> = 1/2 * | +z > + i*sqrt(3)/2 * | -z >##
And we wish to know ##<S_x>##, where ##|+x > = 1/sqrt(2)*|+z> + 1/sqrt(2)*|-z>##
Since there is not an imaginary component for |+x>, I don't see how I can calculate ##<+x | phi >##; there is not an i to negate for ##|+x>## to acquire the complex conjugate <+x|. Perhaps I don't understand the complex conjugation part well enough - equal magnitude and opposite sign, yes?
So, then when I'm calculating ##<+x | phi >## according to the example, I wind up with an expectation value with an imaginary component. Which I don't think is correct.
Can anybody help point out where I have gone wrong?
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