Fund Quantum Mechanics Lect &amp; HW Solutions 26

# Fund Quantum Mechanics Lect &amp; HW Solutions 26 - 8...

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Unformatted text preview: 8 CHAPTER 2. MATHEMATICAL PREREQUISITES The equivalent of a unit vector for functions is not the function 1, it is the Dirac delta function. This function will be discussed in detail later, but simply put, it is a single, inﬁnitely high spike. 2.3 2.3.1 The Dot, oops, INNER Product Solution dot-a Question: Find the following inner product of the two vectors: 1+i 2−i 2i 3 Answer: Take complex conjugates at the left and sum products of corresponding components as in (1 − i) × (2i) + (2 + i) × 3 = 2i + 2 + 6 + 3i = 8 + 5i 2.3.2 Solution dot-b Question: Find the length of the vector 1+i 3 Answer: Take the square root of the inner product of the vector with itself: 1+i 3 1+i 3 which works out like (1 − i)(1 + i) + (3)(3) = √ 1 − i2 + 9 = √ 11 ...
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