EdTddlmZmZmZddlmZmZmZmZm Z ddl m Z dZ dZ dZdS))SpiRational)hermitesqrtexp factorialAbs)hbarcTtt||||g\}}}}||ztz }|tz t ddzt dd|zt |zz z}|t| |dzzdz zt|t ||zzS)aZ 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)) ) maprr rrrr rr)nxmomeganuCs 4lib/python3.11/site-packages/sympy/physics/qho_1d.pypsi_nrs8Q1e,--NAq!U UT B B!Q$q!Q$y||*;'<"="==A sB319a<  71d2hhqj#9#9 99c6t|z|tjzzS)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 rHalf)rrs rE_nr*s: %<1qv: &&rctt|dz dz ||zztt|z S)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 )ralphas rcoherent_staterJs? UQq ! !5!8 ,T)A,,-?-? ??rN) sympy.corerrrsympy.functionsrrrr r sympy.physics.quantum.constantsr rrrrrr$s&&&&&&&&&&>>>>>>>>>>>>>>000000!:!:!:H'''@@@@@@r