Hello, I'm trying to plot a normalized wave function of a free particle. My problem is normalizing the function. But get nothin. I use the following values, (10,100,10,10)

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ajri 2023-12-11

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https://ww2.mathworks.cn/matlabcentral/answers/2059049-hello-i-m-trying-to-plot-a-normalized-wave-function-of-a-free-particle-my-problem-is-normalizing-t

评论： ajri 2023-12-11

function Vogfunktion(Dx, n, m,T)
V = 1;
h_bar = 1.054 * 10^-34;
x = linspace(0 , n*Dx, n);
F =zeros(1,n);
for i = 1:n
    
    for E = 1:n
        V = V + T*i;   
        k = sqrt(2*m*(E+V)/(h_bar^2));   
        psi_i = (sin(k*Dx*(i+1)) + sin(k*Dx*(i-1))/(2 + (Dx^2)* (2*m/h_bar^2)));
        Norm = sqrt(1/trapz(psi_i));
        if Norm ~= 0
            F(i) = Norm;
        end
    end
end
plot(x,F)
ylim([-5,5]);
xlim([0,2*Dx*i]);
ylabel('psi')
xlabel('strÃ¤cka')

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Walter Roberson 2023-12-11

What are size() of your inputs?

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Answer 1

Walter Roberson 2023-12-11

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https://ww2.mathworks.cn/matlabcentral/answers/2059049-hello-i-m-trying-to-plot-a-normalized-wave-function-of-a-free-particle-my-problem-is-normalizing-t#answer_1369204

在 MATLAB Online 中打开

psi_i = (sin(k*Dx*(i+1)) + sin(k*Dx*(i-1))/(2 + (Dx^2)* (2*m/h_bar^2)));

Unless your m is non-scalar, or your Dx is a non-scalar square array, then your psi_i would either error or return a scalar.

Norm = sqrt(1/trapz(psi_i));

trapz() of a scalar is 0. 1/0 is inf. sqrt(inf) is inf.

In order for 1/trapz(psi_1) to be 0 (following test) then the trapz() would have to return inf. You might be able to get NaN for psi_i (such as if Dx is inf then sin(inf) is NaN) but you would have a hard time getting inf out of there. So Norm is not going to be 0.

        if Norm ~= 0
            F(i) = Norm;
        end

You are inside a for E loop but are assigning to F(i) . Except for the case where somehow some of the E values lead to Norm 0 (which would require that the trapz be inf) then you are overwriting all of F(i) for each E value, and the final result would be the same as if you had only executed the last for E iteration.