<div dir="ltr">Dear Stefano,<br><br>Thanks for the nice explanation.<br>Can you please suggest some "old" quantum mechanics books or some other reading materials where they deal with such issues?<br><br>With regards,<br>
Prasenjit.<br><br><div class="gmail_quote">2008/8/11 Stefano Baroni <span dir="ltr"><<a href="mailto:baroni@sissa.it">baroni@sissa.it</a>></span><br><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
Dear Wenmei:<br>
<br>
besides the very sound suggestion by Hande, I would also recommend<br>
that you take a glance at any (possibly, old) textbook in elementary<br>
quantum mechanics. Why old? Because modern texts often given<br>
elementary stuff for granted, which usually it is not.<br>
<br>
Coming to the specific issue that you raise. The number of nodes in<br>
the solution of a 1D Schroedinger equation depends on the energy<br>
parameter. The lower the energy, the fewer the nodes. Of course, for<br>
an arbitrary energy parameter the resulting wavefunction is not<br>
normalizable, that is why it has to be discarded, but for very<br>
special, discrete, values, and energy is quantized. It is interesting<br>
to understand "intuitively" how quantization of energy comes about. As<br>
you rise the energy from any given value, the outer node moves out<br>
furthhr and futher from the origin, but the number of nodes stays<br>
constant if you do not change the energy too much. If the energy is<br>
raised too much, a further node will appear. For some critical value<br>
of the energy, the "extra" node will be at infinity: that's when an<br>
energy eigenvalue is crossed.<br>
<br>
I do not expect that, if you have never heard about similar<br>
arguments, you will understand mine, which have been stated rather<br>
sloppily. Actually, if you decide to study this matter in a serious<br>
book, your ability to understand my "sloppy arguments" will be a check<br>
of your actual understanding of the serious arguments expounded in the<br>
book.<br>
<br>
Hope this helps, a bit<br>
<font color="#888888">Stefano<br>
</font><div><div></div><div class="Wj3C7c"><br>
On Aug 11, 2008, at 6:36 PM, Hande Ustunel wrote:<br>
<br>
> Dear Wenmei,<br>
><br>
> I usually look at the output of the all-electron calculation and<br>
> choose an<br>
> energy close to the ae orbital energy. Once I manage to generate the<br>
> pseudopotential I go as far away as possible from that reference<br>
> without<br>
> upsetting the code.<br>
><br>
> Hope this helps...<br>
> Hande<br>
><br>
> On Tue, 12 Aug 2008, [gb2312] 明文美 wrote:<br>
><br>
>><br>
>> Dear all:<br>
>><br>
>> I want to generate my own RRKJ type ultrasoft pseudopotential<br>
>> with atomic code in PWSCF,<br>
>> I encountered a very confusing situation:<br>
>><br>
>> when I chose -0.20Ry as the second energy used to pseudize the 5s<br>
>> orbit, the ld1.x always complains :<br>
>> =================================================<br>
>> from gener_pseudo : error # 1 too many nodes<br>
>> =================================================<br>
>> however if I change the energy to be -0.50Ry, the corresponding<br>
>> complain disappeared.<br>
>><br>
>> How should I choose these energy parameters to generate a good<br>
>> pseudopotential and how should I have a<br>
>> correct understanding of these parameters?<br>
>><br>
>> Thanks very much .<br>
>><br>
>> Wenmei<br>
>><br>
>> My &inputp file is also listed as :<br>
>><br>
>> 64D 3 2 10 0.00 1.00 2.004D 3 2 0 -0.20 1.00<br>
>> 2.005S 1 0 2 0.00 2.00 2.505S 1 0 0 -0.50 2.00<br>
>> 2.505P 2 1 3 0.00 2.66 2.985P 2 1 0 -0.20 2.66<br>
>> 2.98<br>
>><br>
>><br>
>><br>
>><br>
>><br>
>> _________________________________________________________________<br>
>> 快来看看这些猫咪有多逗，爆笑！<br>
>> <a href="http://cnweb.search.live.com/video/results.aspx?q=%E5%8F%AF%E7%88%B1%E7%8C%AB%E5%92%AA&Form=MEVHAA" target="_blank">http://cnweb.search.live.com/video/results.aspx?q=%E5%8F%AF%E7%88%B1%E7%8C%AB%E5%92%AA&Form=MEVHAA</a><br>
><br>
> --<br>
> Hande Toffoli<br>
> Department of Physics<br>
> Office 439<br>
> Middle East Technical University<br>
> Ankara 06531, Turkey<br>
> Tel : +90 312 210 3264<br>
> <a href="http://www.physics.metu.edu.tr/%7Ehande" target="_blank">http://www.physics.metu.edu.tr/~hande</a><br>
><br>
> _______________________________________________<br>
> Pw_forum mailing list<br>
> <a href="mailto:Pw_forum@pwscf.org">Pw_forum@pwscf.org</a><br>
> <a href="http://www.democritos.it/mailman/listinfo/pw_forum" target="_blank">http://www.democritos.it/mailman/listinfo/pw_forum</a><br>
<br>
_______________________________________________<br>
Pw_forum mailing list<br>
<a href="mailto:Pw_forum@pwscf.org">Pw_forum@pwscf.org</a><br>
<a href="http://www.democritos.it/mailman/listinfo/pw_forum" target="_blank">http://www.democritos.it/mailman/listinfo/pw_forum</a><br>
</div></div></blockquote></div><br><br clear="all"><br>-- <br>PRASENJIT GHOSH,<br>POST-DOC,<br>ROOM NO: 265, MAIN BUILDING,<br>CM SECTION, ICTP,<br>STRADA COSTERIA 11,<br>TRIESTE, 34104,<br>ITALY<br>PHONE: +39 040 2240 369 (O)<br>
+39 3807528672 (M)<br>
</div>