$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}\newcommand{\matrixelement}[3]{\langle#1|#2|#3\rangle}\newcommand{\PP}[2][]{\frac{\partial^2 #1}{\partial #2^2}}\newcommand{\dd}[2][]{\frac{d#1}{d#2}}\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}\newcommand{\average}[2]{\langle#1|#2|#1\rangle}\newcommand{\ket}[1]{\langle #1\rangle}$
$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$ $\newcommand{\matrixelement}[3]{\langle#1|#2|#3\rangle}$$\newcommand{\PP}[2][]{\frac{\partial^2 #1}{\partial #2^2}}$$\newcommand{\dd}[2][]{\frac{d#1}{d#2}}$$\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}$$\newcommand{\average}[2]{\langle#1|#2|#1\rangle}$$\newcommand{\ket}[1]{\langle #1\rangle}$qm-lec-25001
$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$ $\newcommand{\matrixelement}[3]{\langle#1|#2|#3\rangle}$$\newcommand{\PP}[2][]{\frac{\partial^2 #1}{\partial #2^2}}$$\newcommand{\dd}[2][]{\frac{d#1}{d#2}}$$\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}$$\newcommand{\average}[2]{\langle#1|#2|#1\rangle}$$\newcommand{\ket}[1]{\langle #1\rangle}$qm-lec-25002
$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$ $\newcommand{\matrixelement}[3]{\langle#1|#2|#3\rangle}$$\newcommand{\PP}[2][]{\frac{\partial^2 #1}{\partial #2^2}}$$\newcommand{\dd}[2][]{\frac{d#1}{d#2}}$$\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}$$\newcommand{\average}[2]{\langle#1|#2|#1\rangle}$$\newcommand{\ket}[1]{\langle #1\rangle}$qm-lec-25003
$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$ $\newcommand{\matrixelement}[3]{\langle#1|#2|#3\rangle}$$\newcommand{\PP}[2][]{\frac{\partial^2 #1}{\partial #2^2}}$$\newcommand{\dd}[2][]{\frac{d#1}{d#2}}$$\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}$$\newcommand{\average}[2]{\langle#1|#2|#1\rangle}$$\newcommand{\ket}[1]{\langle #1\rangle}$qm-lec-25004
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