ó Ąź™\c@ s‰ddlmZmZddlmZmZmZddlmZm Z m Z m Z m Z ddl mZd„Zd„Zd„ZdS( i˙˙˙˙(tprint_functiontdivision(tStpitRational(thermitetsqrttexpt factorialtAbs(thbarcC s›tt||||gƒ\}}}}||t}|ttdƒdtdd|t|ƒƒ}|t| |ddƒt|t|ƒ|ƒS(sK Returns the wavefunction psi_{n} for the One-dimensional harmonic oscillator. ``n`` the "nodal" quantum number. Corresponds to the number of nodes in the wavefunction. n >= 0 ``x`` x coordinate ``m`` mass of the particle ``omega`` angular frequency of the oscillator Examples ======== >>> from sympy.physics.qho_1d import psi_n >>> from sympy import var >>> var("x m omega") (x, m, omega) >>> psi_n(0, x, m, omega) (m*omega)**(1/4)*exp(-m*omega*x**2/(2*hbar))/(hbar**(1/4)*pi**(1/4)) iii(tmapRR RRRRR(tntxtmtomegatnutC((s3lib/python2.7/site-packages/sympy/physics/qho_1d.pytpsi_ns'4cC st||tddƒS(sú Returns the Energy of the One-dimensional harmonic oscillator ``n`` the "nodal" quantum number ``omega`` the harmonic oscillator angular frequency The unit of the returned value matches the unit of hw, since the energy is calculated as: E_n = hbar * omega*(n + 1/2) Examples ======== >>> from sympy.physics.qho_1d import E_n >>> from sympy import var >>> var("x omega") (x, omega) >>> E_n(x, omega) hbar*omega*(x + 1/2) ii(R R(R R((s3lib/python2.7/site-packages/sympy/physics/qho_1d.pytE_n+scC s1tt|ƒd dƒ||tt|ƒƒS(sń Returns for the coherent states of 1D harmonic oscillator. See https://en.wikipedia.org/wiki/Coherent_states ``n`` the "nodal" quantum number ``alpha`` the eigen value of annihilation operator i(RR RR(R talpha((s3lib/python2.7/site-packages/sympy/physics/qho_1d.pytcoherent_stateGs N(t __future__RRt sympy.coreRRRtsympy.functionsRRRRR tsympy.physics.quantum.constantsR RRR(((s3lib/python2.7/site-packages/sympy/physics/qho_1d.pyts ( #