Solve the Maxwell’s equations and Schrodinger’s equation but avoiding the Sommer | Physics TomorrowAbstract:: Solving Maxwell’s equation and Schrodinger’s equation is usually completed in the frequencydomain. In the frequency domain, the two equations can be solved by Green’s function method.Maxwell equation and Schrodinger equation can be simplified into the Helmholtz equation, and thenthe Helmholtz equation is solved by Green’s function method. Both Green’s function methodsrequire Sommerfeld radiation conditions. Sommerfeld radiation condition requires that thesolution of the equation is equivalent to an attenuated plane wave on an infinite boundary.However, when we solve the Helmholtz equation, we often want to obtain the asymptoticbehaviour of the far-field. The Sommerfeld radiation condition directly specifies the far-fieldasymptotic behaviour of the field, rather than the asymptotic behaviour obtained by calculation. Inthis way, the Sommerfeld radiation condition makes the process of solving differential equationsunreasonable. If there are no other better methods, then we must use Sommerfeld radiationconditions. In addition, the Sommerfeld radiation condition is a strict frequency domaincondition. As long as the frequency of the solution deviates from the frequency of Green’sfunction, the effectiveness of the solution is greatly reduced. The electromagnetic field signals weencounter are usually signalled with specific frequency bands. Green’s function is a functionwith a fixed frequency. In this way, the frequency of the electromagnetic field signal may deviatefrom the frequency of Green’s function, so it can not fully meet the Sommerfeld radiationcondition. So we can’t prove that we got the right solution. In this paper, Maxwell’s equationsand Schrodinger’s equations are solved directly in the time domain. A new method similar to Green’sfunction method is introduced in the time domain. In this method, the new Green’s function andelectromagnetic field adopt different waves. For example, if the electromagnetic signal is aretarded wave, Green’s function uses an advanced wave. If the electromagnetic signal is anadvanced wave, Green’s function uses a retarded wave. Therefore, at the infinite boundary,the retarded wave and the advanced wave do not arrive at the same time, so they are not zero atthe same time, so their inner product is zero. That is, the surface integral is zero, which avoidsSommerfeld and similar radiation conditions. Another advantage of this new method is that it isinsensitive to frequency, which means that the effectiveness of the solution is guaranteed even ifthe frequency of the solution is different from that of Green’s function.