#!/usr/bin/perl
use Net::Twitter;
$|=1;
unless(@ARGV){
print "Usage: $0 twitter_id [sleep_seconds]\n";
exit 0;
}
my ($follow,$sleeper) = @ARGV;
# No account needed for this.
my $twit = Net::Twitter->new(username => 'MYNAME', password => 'XXX');
$p=1;
while(1){
my $result = $twit->user_timeline({id => $follow, page => $p});
foreach my $tweet (@{$result}){
print "At ", $tweet->{'created_at'},"\n";
print $tweet->{'text'},"\n\n";
}
++$p;
sleep $sleeper if $sleeper;
}
You might have to install the Net::Twitter module. This is most easily done as
sudo perl -MCPAN -e shell
and then (possibly after answering a few questions)
install Net::Twitter
is a canonical variable the conjugate variabel is determined by 
. What I had not realized is that you could for example take 
and obtain the same fundamental Poisson brackets (and consequently commuation relations after quantization). Similarly, you could add any function 
to the momentum without changing the commutation relations. 
by the derivative formula, add 
to the action. The most general change would be to add 
. 
, the action of a charge 
particle changes by 
. Thus our change in Lagrangian (with a corresponding change in the canonical momentum) can be viewed as a gauge transformation (even if no gauge field is around one could add a trivial one). Correspondingly, the wave function would have to be changed to 
as acting on 
by a canocially quantized 
is the same as 
acted on by 
-angle 
being the most prominent example. How would that appear in our much simpler quantum mechanics example? Here, it is important to remember that one should only use gauge transformations that are trivial at infinity. Here, if you change the phase of the wave function too wildly at 
you might leave the good part of the Hilbert space: For example the kinetic energy being an unbounded operator is not defined on all of Hilbert space but only on a dense subspace (most often taken to be some Sobolev space). And that you might leave by adding a wild phase and end up in a different self adjoint extension of the kinetic energy. 
-th level of the hydrogen atom has energy proportional to 
. This level has degeneracy 
since 
runs from 1 to 
then runs from 
to 
. First, we thought that this might be a function named after some 19th century mathematician but mathematica told us its name is actually 
since the exponent quickly approaches 1 for every positive 
. 
m and the radius grows like 
. However, at room temperature, Boltzmann exponent 
and 
. Thus, to balance the Boltzmann suppression of the higher levels compared to the ground state one has to take into account at the order of 
states and not just the first 
. Or put differently, one should use and exponentially large cavity. Otherwise the partition function is essentially cut off at 
. To simplify things, this is only first order in time and I would like to view a second order term already as "small" correction. The higher order equation would then be 
with small 
. 
and finds 
. For small 
which blows up and 
which approaches the solution of the "classical equation". 
unless the initial data satisfies the classical equation 
. 
differs from the "classical exponent" 
by order 
for 
. On the axis that goes into the picture there is a parameter for the initial conditions which is 
for data satisfying the classical equation initially. You can see that this parameter determines if 
or 
over short time. Only the classical initial data stays small for much longer. 
Posts
