- #1
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Whenever I write equations in an align they end up very messed up. I have attached picture of how they look. How do I get the equations to start at the left and not suddenly to the right?
My align environment says:
\langle x^2 \rangle = \int_{-\infty}^{\infty}e^{-\mid \alpha_{0}\mid^{2}}\sum_{n=0}^{\infty}\frac{(\alpha_{0}e^{i\omega t})^n}{\sqrt{n!}}\psi_{n}(x)\frac{\hbar}{2m\omega}(a_{+}+a_{-})^2\sum_{m=0}^{\infty}\frac{(\alpha_{0}e^{-i\omega t})^m}{\sqrt{m!}}\psi_{m}(x)dx \\
= \frac{\hbar}{2m\omega}e^{-\mid \alpha_{0}\mid^{2}}\int_{-\infty}^{\infty}\sum_{n=0}^{\infty}\frac{(\alpha_{0}e^{i\omega t})^n}{\sqrt{n!}}\psi_{n}(x)(a_{+}^2+a_{-}^2+a_{+}a_{-}+a_{-}a_{+})\sum_{m=0}^{\infty}\frac{(\alpha_{0}e^{-i\omega t})^m}{\sqrt{m!}}\psi_{m}(x)dx\\ = \frac{\hbar}{2m\omega}e^{-\mid \alpha_{0}\mid^{2}}\int_{-\infty}^{\infty}\sum_{n=0}^{\infty}[a_{+}^2\frac{(\alpha_{0}e^{-i\omega t})^n}{\sqrt{n!}}\psi_{n}(x)]^{*}[(a_{+}^2+n+n+1)\sum_{m=0}^{\infty}\frac{(\alpha_{0}e^{-i\omega t})^m}{\sqrt{m!}}\psi_{m}(x)]dx\\
=\frac{\hbar}{2m\omega}e^{-\mid \alpha_{0}\mid^{2}}\int_{-\infty}^{\infty}\sum_{n=0}^{\infty}[\frac{\sqrt{n+1}\sqrt{n+2}(\alpha_{0}e^{-i\omega t})^n}{\sqrt{n!}}\psi_{n+2}(x)]^{*}[\sum_{m=0}^{\infty})(2n+1)\frac{(\alpha_{0}e^{-i\omega t})^m}{\sqrt{m!}}\psi_{m}(x)+\sum_{m=0}^{\infty}\sqrt{n+1}\sqrt{n+2}\frac{(\alpha_{0}e^{-i\omega t})^m}{\sqrt{m!}}\psi_{m+2}(x)]dx]\\ =
\end{align*}
Seems messy, but all I want you to is identify what is making the equations start all the way at the left and go out of the margin.
My align environment says:
\langle x^2 \rangle = \int_{-\infty}^{\infty}e^{-\mid \alpha_{0}\mid^{2}}\sum_{n=0}^{\infty}\frac{(\alpha_{0}e^{i\omega t})^n}{\sqrt{n!}}\psi_{n}(x)\frac{\hbar}{2m\omega}(a_{+}+a_{-})^2\sum_{m=0}^{\infty}\frac{(\alpha_{0}e^{-i\omega t})^m}{\sqrt{m!}}\psi_{m}(x)dx \\
= \frac{\hbar}{2m\omega}e^{-\mid \alpha_{0}\mid^{2}}\int_{-\infty}^{\infty}\sum_{n=0}^{\infty}\frac{(\alpha_{0}e^{i\omega t})^n}{\sqrt{n!}}\psi_{n}(x)(a_{+}^2+a_{-}^2+a_{+}a_{-}+a_{-}a_{+})\sum_{m=0}^{\infty}\frac{(\alpha_{0}e^{-i\omega t})^m}{\sqrt{m!}}\psi_{m}(x)dx\\ = \frac{\hbar}{2m\omega}e^{-\mid \alpha_{0}\mid^{2}}\int_{-\infty}^{\infty}\sum_{n=0}^{\infty}[a_{+}^2\frac{(\alpha_{0}e^{-i\omega t})^n}{\sqrt{n!}}\psi_{n}(x)]^{*}[(a_{+}^2+n+n+1)\sum_{m=0}^{\infty}\frac{(\alpha_{0}e^{-i\omega t})^m}{\sqrt{m!}}\psi_{m}(x)]dx\\
=\frac{\hbar}{2m\omega}e^{-\mid \alpha_{0}\mid^{2}}\int_{-\infty}^{\infty}\sum_{n=0}^{\infty}[\frac{\sqrt{n+1}\sqrt{n+2}(\alpha_{0}e^{-i\omega t})^n}{\sqrt{n!}}\psi_{n+2}(x)]^{*}[\sum_{m=0}^{\infty})(2n+1)\frac{(\alpha_{0}e^{-i\omega t})^m}{\sqrt{m!}}\psi_{m}(x)+\sum_{m=0}^{\infty}\sqrt{n+1}\sqrt{n+2}\frac{(\alpha_{0}e^{-i\omega t})^m}{\sqrt{m!}}\psi_{m+2}(x)]dx]\\ =
\end{align*}
Seems messy, but all I want you to is identify what is making the equations start all the way at the left and go out of the margin.