- #1
dimensionless
- 462
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I'm trying to figure out this equation.
[tex]
{\Psi} = Ae^{-a(bx-ct)^2}
[/tex]
I've expanded this to
[tex]
{\Psi} = Ae^{-ab^2x^2-abxct-ac^2t^2}
[/tex]
When I try to find the derivative I get this
[tex]
\left(\newcommand {\pd}[3]{ \frac{ \partial^{#3}{#1} }{ \partial {#2}^{#3} } }
\pd{\Psi}{t}{}\right)_x = (-2ac^2t-abxc)Ae^{-ab^2x^2-abxct-ac^2t^2}
[/tex]
I should get this instead
[tex]
\left(\newcommand {\pd}[3]{ \frac{ \partial^{#3}{#1} }{ \partial {#2}^{#3} } }
\pd{\Psi}{t}{}\right)_x = (-2abcx-2ac^2t)Ae^{-ab^2x^2-abxct-ac^2t^2}
[/tex]
Can anyone tell me where my error is and how I can fix it?
[tex]
{\Psi} = Ae^{-a(bx-ct)^2}
[/tex]
I've expanded this to
[tex]
{\Psi} = Ae^{-ab^2x^2-abxct-ac^2t^2}
[/tex]
When I try to find the derivative I get this
[tex]
\left(\newcommand {\pd}[3]{ \frac{ \partial^{#3}{#1} }{ \partial {#2}^{#3} } }
\pd{\Psi}{t}{}\right)_x = (-2ac^2t-abxc)Ae^{-ab^2x^2-abxct-ac^2t^2}
[/tex]
I should get this instead
[tex]
\left(\newcommand {\pd}[3]{ \frac{ \partial^{#3}{#1} }{ \partial {#2}^{#3} } }
\pd{\Psi}{t}{}\right)_x = (-2abcx-2ac^2t)Ae^{-ab^2x^2-abxct-ac^2t^2}
[/tex]
Can anyone tell me where my error is and how I can fix it?
Last edited: