Posts

Showing posts from September 12, 2018

An imaginary coefficient in heat equation ensures no special direction in time?

Image
Clash Royale CLAN TAG #URR8PPP up vote 9 down vote favorite In Pauli(1973): Wave Mechanics (Pauli lectures on physics Volume 5) he derives on page 4 the Schrödinger equation (similar to Tong: Lectures on QFT, p. 42) $$ nabla^2 psi' + i frac2mhfracpartial psi'partial t - frac1c^2fracpartial^2 psi' partial t^2 = 0 $$ (the last term vanishes in the limit $c rightarrow infty$) and makes the following peculiar remark: Aside from the imaginary coefficient, it corresponds to the equation of heat conduction. The imaginary coefficient assures that there is no special direction in time; [2.11] is invariant under the transformation $t rightarrow -t, psi' rightarrow psi'^*$, whereby $psi^*psi$ remains unchanged. What does he mean by "the imaginary coefficient assures there is no special direction in time"? Does the real heat equation without imaginary coefficient have a special direction in time? What does direction mean? Forward or backward? Or a d

Calcareous deposits in arid soil?

Image
Clash Royale CLAN TAG #URR8PPP up vote 4 down vote favorite I read this line in my textbook: Lower Horizons of arid soil are occupied by calcareous deposits called kankar because of the increasing calcium content downwards. My question is that why only in arid soil? Increase of calcium content will led to formation of kankars in other types of soil also, then why it happens only in arid soil? soil share | improve this question asked yesterday Vandana 45 3 add a comment  |  up vote 4 down vote favorite I read this line in my textbook: Lower Horizons of arid soil are occupied by calcareous deposits called kankar because of the increasing calcium content downwards. My question is that why only in arid soil? Increase of calcium content will led to formation of kankars in other types of soil also, then why it happens only in arid soil? soil share | improve this question asked yesterday Vandana 45 3