Codes for coherent state function?

Summation n=0 to10 exp-abs(alpha)^2*alpha^n/sqrtfactorial(n)

Answer 1

[Walter Roberson]

syms alpha n
result = symsum(exp(-abs(alpha)^2 * alpha^n / sqrt(factorial(n)) ), n, 0, 10)

result = 

[Abu Zar]

if we put alpha=0.5 the code become?

syms alpha n

result = symsum(exp(-abs(alpha)^2 * alpha^n / sqrt(factorial(n)) ),aplha,0.5, n, 0, 10)

[Walter Roberson]

syms n
alpha = sym(0.5)
result = symsum(exp(-abs(alpha)^2 * alpha^n / sqrt(factorial(n)) ), n, 0, 10)

[Abu Zar]

Thank you very much

[Abu Zar]

Hello sir,can i use alpha=0.5 instead of alpha=sym(0.5)?

[Walter Roberson]

On the special case that alpha is a negative power of 2 (0.5, 0.25, 0.125 and so on) greater than 2^-512 you can use the exact decimal equivalent for alpha without using sym()

The same is true if alpha is an exact integer multiple of a negative power of 2 and the multiple does not exceed 2^53 and you specify alpha as a fraction, such as alpha = 83617/2^37. However the larger the denominator, the higher the risk that matlab might approximate as a different fraction.

[Abu Zar]

I Just use alpha=0.05

And i want calculate different alpha using a list and “ for “ iteration to calculate the result , one by one.

help me with one example thank you very much.

[Walter Roberson]

format long g
syms n
alpha = sym(0.05)

alpha = 

result1 = symsum(exp(-abs(alpha)^2 * alpha^n / sqrt(factorial(n)) ), n, 0, 10)

result1 = 

syms n
alpha = 0.05

alpha = 
                      0.05

result2 = symsum(exp(-abs(alpha)^2 * alpha^n / sqrt(factorial(n)) ), n, 0, 10)

result2 = 

result1 - result2

ans = 

0

Alpha = rand

Alpha = 
         0.691938609323685

alpha = sym(Alpha)

alpha = 

result3 = symsum(exp(-abs(alpha)^2 * alpha^n / sqrt(factorial(n)) ), n, 0, 10)

result3 = 

alpha = Alpha

alpha = 
         0.691938609323685

result4 = symsum(exp(-abs(alpha)^2 * alpha^n / sqrt(factorial(n)) ), n, 0, 10)

result4 = 

result3 - result4

ans = 

double(ans)

ans = 
     -9.46009976357279e-18

This shows that for some alpha values you can get away with using numeric alpha, but for other alpha values you need to use sym() to get an accurate answer.

In particular if your input alpha has more than 26 bits of precision, the automatic conversion of abs(alpha)^2 might not match abs(sym(alpha))^2

[Walter Roberson]

format long g
syms n
alpha = linspace(0.01, 0.99, 25);
inner = exp(-abs(sym(alpha)).^2 .* sym(alpha).^n ./ sqrt(factorial(n)) )

inner = 

resultsym = sum(subs(inner, n, (0:10).'),1).';
result = double(resultsym)

result = 25×1

10.9998989978882 10.9972830981744 10.9908097750576 10.980037695147 10.9645002860003 10.9437012720096 10.9171106809702 10.8841614122063 10.8442464792823 10.7967170574898

plot(alpha, result)

[Abu Zar]

Hi , i see you create "25 X 1'',how we can create "25 X 25".

[Zar]

v.nice

[Walter Roberson]

remove the sum() from resultsym to get length(alpha) by length(0:11), which would be removing the summation from the formula

[Abu Zar]

Hello sir,

I created this m.file to draw plot alpha vs Vnorm , but the vector is not the same length,I requetd you to look this file for my help to draw th plot.

Thank you