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Fund Quantum Mechanics Lect &amp; HW Solutions 54

# Fund Quantum Mechanics Lect &amp; HW Solutions 54 - 36...

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36 CHAPTER 3. BASIC IDEAS OF QUANTUM MECHANICS system (¯ x, ¯ y, z ) that is rotated 45 degrees counter-clockwise around the z -axis compared to the original ( x, y, z ) coordinate system. Answer: Take the rotated coordinates to be ¯ x and ¯ y as shown: a A x y ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ² ³ ³ ³ ³ ³ ³ ³ ³ ³ ³ ³ ³ ³ ³ ³ ´ ¯ x ¯ y A vector displacement of magnitude x in the x -direction has a component along the ¯ x -axis of magnitude x cos 45 , equivalent to x/ 2. Similarly, a vector displacement of magnitude y in the y -direction has a component along the ¯ x -axis of magnitude y cos 45 , equivalent to y/ 2. So in general, for any point ( x, y ), ¯ x = x + y 2 . Similarly you get
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