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In Tao's book, page 84, he stated the conservation law for the linear Schrodinger's equation $i partial_t u+ frac{1}{2}Delta u = 0$. But there are other resources treating the equation as $partial_t{u} + Delta u$.

I verified the first equation in the conservation law is the same for both situations. But it seems that the second one is dependent on the coefficients. I wonder what is the right conservation law for $partial_t{u} + Delta u = 0$.

real-analysis pde elliptic-equations

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asked Mar 10 at 2:10

zachzach

946

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0

$begingroup$

In Tao's book, page 84, he stated the conservation law for the linear Schrodinger's equation $i partial_t u+ frac{1}{2}Delta u = 0$. But there are other resources treating the equation as $partial_t{u} + Delta u$.

I verified the first equation in the conservation law is the same for both situations. But it seems that the second one is dependent on the coefficients. I wonder what is the right conservation law for $partial_t{u} + Delta u = 0$.

real-analysis pde elliptic-equations

share|cite|improve this question

asked Mar 10 at 2:10

zachzach

946

$endgroup$

add a comment | 

$begingroup$

In Tao's book, page 84, he stated the conservation law for the linear Schrodinger's equation $i partial_t u+ frac{1}{2}Delta u = 0$. But there are other resources treating the equation as $partial_t{u} + Delta u$.

I verified the first equation in the conservation law is the same for both situations. But it seems that the second one is dependent on the coefficients. I wonder what is the right conservation law for $partial_t{u} + Delta u = 0$.

real-analysis pde elliptic-equations

share|cite|improve this question

asked Mar 10 at 2:10

zachzach

946

$endgroup$

share|cite|improve this question

asked Mar 10 at 2:10

zachzach

946

share|cite|improve this question

asked Mar 10 at 2:10

zachzach

946

asked Mar 10 at 2:10

zachzach

946

asked Mar 10 at 2:10

zachzach

946