o oÇ hÕã@sXddlmZmZmZddlmZmZmZmZm Z ddl m Z dd„Z dd„Z dd „Zd S) é)ÚSÚpiÚRational)ÚhermiteÚsqrtÚexpÚ factorialÚAbs)ÚhbarcCs|tt||||gƒ\}}}}||t}|ttddƒtdd|t|ƒƒ}|t| |ddƒt|t|ƒ|ƒS)aJ Returns the wavefunction psi_{n} for the One-dimensional harmonic oscillator. Parameters ========== 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.abc import m, x, omega >>> psi_n(0, x, m, omega) (m*omega)**(1/4)*exp(-m*omega*x**2/(2*hbar))/(hbar**(1/4)*pi**(1/4)) ééé) Úmaprr rrrrrr)ÚnÚxÚmÚomegaÚnuÚC©rúh/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/sympy/physics/qho_1d.pyÚpsi_ns *,rcCst||tjS)a Returns the Energy of the One-dimensional harmonic oscillator. Parameters ========== n : The "nodal" quantum number. omega : The harmonic oscillator angular frequency. Notes ===== 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.abc import x, omega >>> E_n(x, omega) hbar*omega*(x + 1/2) )r rÚHalf)rrrrrÚE_n*srcCs*tt|ƒd dƒ||tt|ƒƒS)a Returns for the coherent states of 1D harmonic oscillator. See https://en.wikipedia.org/wiki/Coherent_states Parameters ========== n : The "nodal" quantum number. alpha : The eigen value of annihilation operator. r )rr rr)rÚalpharrrÚcoherent_stateJs*rN)Ú sympy.corerrrÚsympy.functionsrrrrr Úsympy.physics.quantum.constantsr rrrrrrrÚs  $