Laplace transform and Fourier transform
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I used the Fourier and Laplace transforms to solve a series of equations. Now I have to use the inverse of these conversions to get the wave function. My question is
$$L^-1(fracddkpsi(k,s))=?fracddkpsi(k,t)$$
$$F(fracddxpsi)=-ikpsi(k)$$ $$F^-1(fracddkpsi(k))=?-ixpsi(x)$$
fourier-analysis laplace-transform fourier-transform
asked Sep 9 at 14:07
Kavoos
63
add a comment |Â
up vote
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I used the Fourier and Laplace transforms to solve a series of equations. Now I have to use the inverse of these conversions to get the wave function. My question is
$$L^-1(fracddkpsi(k,s))=?fracddkpsi(k,t)$$
$$F(fracddxpsi)=-ikpsi(k)$$ $$F^-1(fracddkpsi(k))=?-ixpsi(x)$$
fourier-analysis laplace-transform fourier-transform
asked Sep 9 at 14:07
Kavoos
63
Integrate your equations in $k$ over an interval, and see if you can verify the resulting equations in integrated form. Then see if you can differentiate with respect to the upper limit $k$. That's usually much easier than trying to deal with the derivative expressions.
– DisintegratingByParts
Sep 9 at 16:30
Are written relationships correct?
– Kavoos
Sep 9 at 21:10
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I used the Fourier and Laplace transforms to solve a series of equations. Now I have to use the inverse of these conversions to get the wave function. My question is
$$L^-1(fracddkpsi(k,s))=?fracddkpsi(k,t)$$
$$F(fracddxpsi)=-ikpsi(k)$$ $$F^-1(fracddkpsi(k))=?-ixpsi(x)$$
fourier-analysis laplace-transform fourier-transform
asked Sep 9 at 14:07
Kavoos
63
I used the Fourier and Laplace transforms to solve a series of equations. Now I have to use the inverse of these conversions to get the wave function. My question is
$$L^-1(fracddkpsi(k,s))=?fracddkpsi(k,t)$$
$$F(fracddxpsi)=-ikpsi(k)$$ $$F^-1(fracddkpsi(k))=?-ixpsi(x)$$
fourier-analysis laplace-transform fourier-transform
fourier-analysis laplace-transform fourier-transform
asked Sep 9 at 14:07
Kavoos
63
asked Sep 9 at 14:07
Kavoos
63
asked Sep 9 at 14:07
Kavoos
63
asked Sep 9 at 14:07
Kavoos
63
asked Sep 9 at 14:07
Kavoos
63
63
Integrate your equations in $k$ over an interval, and see if you can verify the resulting equations in integrated form. Then see if you can differentiate with respect to the upper limit $k$. That's usually much easier than trying to deal with the derivative expressions.
– DisintegratingByParts
Sep 9 at 16:30
Are written relationships correct?
– Kavoos
Sep 9 at 21:10
add a comment |Â
Integrate your equations in $k$ over an interval, and see if you can verify the resulting equations in integrated form. Then see if you can differentiate with respect to the upper limit $k$. That's usually much easier than trying to deal with the derivative expressions.
– DisintegratingByParts
Sep 9 at 16:30
Are written relationships correct?
– Kavoos
Sep 9 at 21:10
Integrate your equations in $k$ over an interval, and see if you can verify the resulting equations in integrated form. Then see if you can differentiate with respect to the upper limit $k$. That's usually much easier than trying to deal with the derivative expressions.
– DisintegratingByParts
Sep 9 at 16:30
Integrate your equations in $k$ over an interval, and see if you can verify the resulting equations in integrated form. Then see if you can differentiate with respect to the upper limit $k$. That's usually much easier than trying to deal with the derivative expressions.
– DisintegratingByParts
Sep 9 at 16:30
Are written relationships correct?
– Kavoos
Sep 9 at 21:10
Are written relationships correct?
– Kavoos
Sep 9 at 21:10
add a comment |Â
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Integrate your equations in $k$ over an interval, and see if you can verify the resulting equations in integrated form. Then see if you can differentiate with respect to the upper limit $k$. That's usually much easier than trying to deal with the derivative expressions.
– DisintegratingByParts
Sep 9 at 16:30
Are written relationships correct?
– Kavoos
Sep 9 at 21:10