ó Ąž™\c@ sdddlmZmZddlmZmZmZmZmZddl m Z d„Z d„Z dS(iĸĸĸĸ(tprint_functiontdivision(tsqrttexptStpitI(thbarcC s9t|ƒt|ƒ}}t|t|ƒtdtƒS(s˜ Returns the wavefunction for particle on ring. n is the quantum number, x is the angle, here n can be positive as well as negative which can be used to describe the direction of motion of particle Examples ======== >>> from sympy.physics.pring import wavefunction, energy >>> from sympy import Symbol, integrate, pi >>> x=Symbol("x") >>> wavefunction(1, x) sqrt(2)*exp(I*x)/(2*sqrt(pi)) >>> wavefunction(2, x) sqrt(2)*exp(2*I*x)/(2*sqrt(pi)) >>> wavefunction(3, x) sqrt(2)*exp(3*I*x)/(2*sqrt(pi)) The normalization of the wavefunction is: >>> integrate(wavefunction(2, x)*wavefunction(-2, x), (x, 0, 2*pi)) 1 >>> integrate(wavefunction(4, x)*wavefunction(-4, x), (x, 0, 2*pi)) 1 References ========== .. [1] Atkins, Peter W.; Friedman, Ronald (2005). Molecular Quantum Mechanics (4th ed.). Pages 71-73. i(RRRRR(tntx((s2lib/python2.7/site-packages/sympy/physics/pring.pyt wavefunctions$cC s_t|ƒt|ƒt|ƒ}}}|jrO|dtdd||dStdƒ‚dS(sĪ Returns the energy of the state corresponding to quantum number n. E=(n**2 * (hcross)**2) / (2 * m * r**2) here n is the quantum number, m is the mass of the particle and r is the radius of circle. Examples ======== >>> from sympy.physics.pring import energy >>> from sympy import Symbol >>> m=Symbol("m") >>> r=Symbol("r") >>> energy(1, m, r) hbar**2/(2*m*r**2) >>> energy(2, m, r) 2*hbar**2/(m*r**2) >>> energy(-2, 2.0, 3.0) 0.111111111111111*hbar**2 References ========== .. [1] Atkins, Peter W.; Friedman, Ronald (2005). Molecular Quantum Mechanics (4th ed.). Pages 71-73. is'n' must be integerN(Rt is_integerRt ValueError(Rtmtr((s2lib/python2.7/site-packages/sympy/physics/pring.pytenergy.s&  N( t __future__RRtsympyRRRRRtsympy.physics.quantum.constantsRR R(((s2lib/python2.7/site-packages/sympy/physics/pring.pyts( (