<html><head><style>p{margin-top:0px;margin-bottom:0px;}</style></head><body><div style="font-size:14px; font-family:Gulim,굴림,sans-serif;"><div><span>Thank you for your reply.</span></div><div><br></div><div><span>Looking at the projwfc.x output, the projected atomic states are labeled by l, j, and mj, for example :</span></div><div><span> state # 1: atom 1 (Cs ), wfc 1 (l=0 j=0.5 m_j=-0.5)</span></div><div><span> state # 2: atom 1 (Cs ), wfc 1 (l=0 j=0.5 m_j= 0.5)</span></div><div><span> state # 3: atom 1 (Cs ), wfc 2 (l=1 j=1.5 m_j=-1.5)</span></div><div><span> state # 4: atom 1 (Cs ), wfc 2 (l=1 j=1.5 m_j=-0.5)</span></div><div><span> state # 5: atom 1 (Cs ), wfc 2 (l=1 j=1.5 m_j= 0.5)</span></div><div><span> state # 6: atom 1 (Cs ), wfc 2 (l=1 j=1.5 m_j= 1.5)</span></div><div><span> state # 7: atom 1 (Cs ), wfc 3 (l=1 j=0.5 m_j=-0.5)</span></div><div><span> state # 8: atom 1 (Cs ), wfc 3 (l=1 j=0.5 m_j= 0.5)</span></div><div><span>...</span></div><div><br></div><div><span>Further below, each Bloch state is decomposed in terms of these projected states,</span></div><div><span>e.g.</span></div><div><span>==== e( 1) = -159.62902077 eV ====</span></div><div><span> psi = 0.499*[# 11]+0.499*[# 12]</span></div><div><span> |psi|^2 = 1.000</span></div><div><span>==== e( 2) = -159.62902077 eV ====</span></div><div><span> psi = 0.499*[# 11]+0.499*[# 12]</span></div><div><span> |psi|^2 = 1.000</span></div><div><span>==== e( 3) = -109.66866690 eV ====</span></div><div><span> psi = 0.500*[# 17]+0.500*[# 18]</span></div><div><span> |psi|^2 = 1.000</span></div><div><span>...</span></div><div><br></div><div><span>So, is it correct to interpret this as |C_n,k,l,j,mj|^2=|<phi_n,k,l,j,mj|psi_q.e>|^2</span></div><div><span>rather than in |l,m,s> basis ?</span></div><div><br></div><div><span style="font-weight: bold;">In other words, when spin-orbit coupling is included, should the projwfc.x output be understood in the coupled angular momentum basis |l, j, mj>?</span></div><div><br></div><div style="font-family: Gulim, 굴림, sans-serif; font-size: 14px;">Best regards,</div><div style="font-family: Gulim, 굴림, sans-serif; font-size: 14px;">Gi Myung Park</div><div style="font-family: Gulim, 굴림, sans-serif; font-size: 14px;">Yonsei University</div><p style="font-size:10pt;font-family:sans-serif;padding:0 0 0 10pt"><span>-----Original Message-----</span><br><b>From:</b> "Giovanni Cantele via users"<users@lists.quantum-espresso.org> <br><b>To:</b> "Quantum ESPRESSO users Forum"<users@lists.quantum-espresso.org>; <br><b>Cc:</b> <br><b>Sent:</b> 2026-04-04 (토) 23:33:58 (GMT+09:00)<br><b>Subject:</b> Re: [QE-users] [projwfc.x]<br><br></p><div dir="ltr"><div>Hi,</div><div>in the presence of spin-orbit coupling, as specified here:</div><div><a href="https://www.quantum-espresso.org/Doc/INPUT_PROJWFC.html" rel="noreferrer noopener" target="_blank">https://www.quantum-espresso.org/Doc/INPUT_PROJWFC.html</a></div><div>this is what projwfc.x does:</div><div><br>In the non-collinear, spin-orbit case (i.e. if there is at least one<br>fully relativistic pseudopotential) wavefunctions are projected<br>onto eigenstates of the total angular-momentum.<br>Projected DOS are written to file "filpdos".pdos_atm#N(X)_wfc#M(l_j),<br>where N = atom number , X = atom symbol, M = wfc number, l=s,p,d,f<br>and j is the value of the total angular momentum.<br>In this case the format is:<br> E LDOS(E) PDOS_1(E) ... PDOS_2j+1(E)<br> ...</div><div><br></div><div><br></div><div>The presence of the perturbing spin-robit potential L.S merges spatial orbitals</div><div>with spin orbitals to produce eigenstates of the total angular momentum eigenstates`</div><div>and mz --> Lz, ms --> Sz are no longer good quantum numbers (L.S = (J^2-L^2-S^2)/2 and</div><div>the eigenstates of J^2 and Jz are also eigenstates of L^2 and S^2 but not of Lz and Sz).</div><div><br></div><div>Giovanni</div><div><div dir="ltr"><div dir="ltr"><span style="color:rgb(0,0,0)">-- <br><br>Prof. Giovanni Cantele<br>Dipartimento di Fisica "Ettore Pancini"<br>Universita' degli Studi di Napoli "Federico II"<br>Complesso Universitario M. S. Angelo - Ed. 6<br>Via Cintia, I-80126, Napoli, Italy<br>e-mail: <a href="mailto:giovanni.cantele@unina.it" target="_blank" rel="noreferrer noopener">giovanni.cantele@unina.it</a><br>Phone: +39 081 676910<br><br>Web page: </span><a href="https://sites.google.com/view/giovanni-cantele/home" style="color:rgb(17,85,204)" target="_blank" rel="noreferrer noopener">https://sites.google.com/view/giovanni-cantele/home</a><br></div></div></div><br></div><br><div><div dir="ltr">Il giorno sab 4 apr 2026 alle ore 12:34 박기명 <<a href="mailto:knppkm@naver.com" rel="noreferrer noopener" target="_blank">knppkm@naver.com</a>> ha scritto:<br></div><blockquote style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div><div><div style="font-size:14px;font-family:Gulim,굴림,sans-serif"><div>Dear users,</div><div><br></div><div><span>When performing calculations using projwfc.x, results for "j" and "mj" are obtained.</span></div><div><span>Are "j" and "mj" the total angular moment and the corresponding mj (j, j-1, ..., -j)?</span></div><div><span>Is there a reason why the values for "l" and "m" are not provided?</span></div><div><br></div><div>Best regards,</div><div>Gi Myung Park</div><div>Yonsei University</div></div></div><table style="display:none"><tbody><tr><td></td></tr></tbody></table>_______________________________________________________________________________<br>
The Quantum ESPRESSO Foundation stands in solidarity with all civilians worldwide who are victims of terrorism, military aggression, and indiscriminate warfare.<br>
--------------------------------------------------------------------------------<br>
Quantum ESPRESSO is supported by MaX (<a href="http://www.max-centre.eu" rel="noreferrer noopener" target="_blank">www.max-centre.eu</a>)<br>
users mailing list <a href="mailto:users@lists.quantum-espresso.org" target="_blank" rel="noreferrer noopener">users@lists.quantum-espresso.org</a><br>
<a href="https://lists.quantum-espresso.org/mailman/listinfo/users" rel="noreferrer noopener" target="_blank">https://lists.quantum-espresso.org/mailman/listinfo/users</a></div></blockquote></div>
</div></body></html><table style='display:none'><tr><td><img src="https://mail.naver.com/readReceipt/notify/?img=3mFR1XImW4RopxvrpxmsMrU9FrF0F6kvMop0MqJ4Fxbrp6tmaAvdpAvXtzFXp6UmKAb5W4dQaXkqpBiqtzwGbX3q7NJ9M6ld%2B6dRpBFmb4kqbrY5WXiN.gif" border="0"/></td></tr></table>