This is a manipulated schrondinger equation for quantum harmonic oscillator. And

Question

This is a manipulated schrondinger equation for quantum harmonic oscillator. And the code need a to be in matlab or C++.

a) Write a short computer program that evaluates this integral numerically using the
trapezoid rule for any valid excitation state. Use only basic coding language functions:
arithmetic, loops, comparisons, exponentiation, and standard math functions such as exponentials, logarithms, and trigonometric functions. Attach all computer code and your coding must be commented and easy to understand.

(b) Report the probabilities for n = 0, 1, 2 from your program and discuss the trend as n
gets large. Use a sufficient number of integration points to achieve at least three decimal places of accuracy.

Explanation / Answer

#include<iostream>
#include<cmath>
using namespace std;
double cal(double x)        // function to calculate the integral
{
    double a=1/(1+x*x);
    return a;
}
int main()
{
    int n,i;        //n is used for subintervals
    double a,b,c,sum=0,in;  
    cout<<"Enter the limits of integration, Initial limit,a=";    //to get the limits
    cin>>a;
    cout<<"Final limit, b=";
    cin>>b;
    cout<<"Enter the no. of subintervals, n=";          
    cin>>n;                         //accepting no of subintervals
    double x[n+1],y[n+1];  
    c=(b-a)/n;                //calculating width of the subintervals
    for (i=0;i<=n;i++)          
    {                    //here evaluation of x0 to xn and y0 to yn is done
        x[i]=a+i*h;            //and their value is stored in arrays
        y[i]=cal(x[i]);
    }
    for (i=1;i<n;i++)            //loop to evaluate c*(y1+...+yn-1)
    {
        sum=sum+c*y[i];
    }
    in=c/2.0*(y[0]+y[n])+sum;      
    cout<<"The definite integral is "<<in<<endl;
    return 0;
}

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