![]() ![]() (8) to getĪs the wave function depends on quantum number π so we write it ψ n. This will give a zero wave function every where which means particle is not inside the box. ![]() (9) because then both A and B would be zero. (iii) Determination of Energy of ParticleĪpply Boundary condition of eq.(5) to eq.(4)Īpplying the boundary condition of eq.(6) to eq.(8) ,we haveĪ Cannot be zero in eq. These equations are known as Boundary conditions. ![]() We know that the wave function must be continuous at the boundaries of potential well at x=0 and x=L, i.e. So the probability of finding the particle outside the box is zero i.e.ψx=0 outside the box. The particle will always remain inside the box because of infinite potential barrier at the walls. Where A and B are arbitrary conditions and these will be determined by the boundary conditions. K is called the Propagation constant of the wave associated with particle and it has dimensions reciprocal of length. Therefore the Schrodinger equation in this region becomes Here we have changed partial derivatives in to exact because equation now contains only one variable i.e x-Co-ordinate. The one-dimensional time independent Schrodinger wave equation is given by ![]()
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