How can I plot this function?

Hi all

I have this function ,

$W(x,p)=\sqrt{\frac{\pi}{2}}exp(\frac{(-p^2)-4p\lambda_I-4\lambda_{I}^2-16x^2+16\lambda_Rx+16d}{8})$

where x and p any real number and $\lambda$ is complex number

How can I plot this function by using matlab.

Iappreciate any help

Answer 1

[Chunru]

% parameters (use your values)
lambdaR = 1;
lambdaI = -1;
d = 3;
p = 2;

x = -10:.1:10;
w = sqrt(pi/2)*exp((-p^2-4*p*lambdaI-4*lambdaI^2-16*x.^2+16*lambdaR*x+16*d)/8);

plot(x, w)

Answer 2

[Star Strider]

This requires a surface plot with separate plots for the real and imaginary components —

lambdaI = randn;                             % Random Complex Scalar
lambdaR = randn;                             % Random Complex Scalar
d = randn;                                              % Random Scalar
W = @(x,p) sqrt(pi/2) * exp((-p.^2 -4*p.*lambdaI -4*lambdaI.^2 - 16*x.^2 + 16*lambdaR.*x + 16*d)/8);

x = linspace(-2.5, 2.5, 50);
p = linspace(-5, 5, 50);
[X,P] = ndgrid(x,p);

figure
surfc(X,P,real(W(X,P)))
grid on
colormap(turbo)
xlabel('x')
ylabel('p')
zlabel('W(x,p)')

.

[Torsten]

@Star Strider

lambda_R and lambda_I are real numbers (real and imaginary part of lambda)

[Star Strider]

@Torsten — Early here. Missed that. Thanks! Changed.

[Torsten]

@Star Strider

I think there is nothing complex in W (lambda_I and lambda_R are both real).

Thus the plot should be over real tuples (lambda_R,lambda_I), I guess.

But maybe the OP can clarify.

[Star Strider]

@Torsten — I fixed the and to both be real, however the variables are ‘x’ and ‘p’ so I plotted the surface with those as . I have no idea if λ is a vector, so I assume it’s a scalar here.