I have the next list :
{{0.1, -15.3512}, {0.2, -115.194}, {0.3, -133.702}, {0.4, -140.201}, \
{0.5, -143.232}, {0.6, -144.903}, {0.7, -145.935}, {0.8, -146.63}, \{0.9,
-147.132}, {1., -147.518}, {1.1, -147.828}, {1.2, -148.089}, \{1.3,
-148.318}, {1.4, -148.523}, {1.5, -148.716}, {1.6, -148.893}, \{1.7,
-149.054}, {1.8, -149.223}, {1.9, -149.379}, {2., -149.528}, \{2.1,
-149.671}, {2.2, -149.804}, {2.3, -149.929}, {2.4, -150.043}, \{2.5,
-150.143}, {2.6, -150.225}, {2.7, -150.287}, {2.8, -150.324}, \{2.9,
-150.329}, {3., -150.298}, {3.1, -150.224}, {3.2, -150.098}, \{3.3,
-149.911}, {3.4, -149.653}, {3.5, -149.315}, {3.6, -148.88}, \{3.7,
-148.344}, {3.8, -147.686}, {3.9, -146.889}, {4., -145.937}, \
{4.1, -144.816}, {4.2, -143.509}, {4.3, -141.997}, {4.4, -140.263}, \{4.5,
-138.307}, {4.6, -136.061}, {4.7, -133.564}, {4.8, -130.786}, \{4.9,
-127.716}, {5., -124.349}, {5.1, -120.684}, {5.2, -116.715}, \{5.3,
-112.457}, {5.4, -107.914}, {5.5, -103.102}, {5.6, -98.0415}, \{5.7,
-92.7544}, {5.8, -87.273}, {5.9, -81.6295}, {6., -75.8572}, \{6.1,
-69.9991}, {6.2, -64.092}, {6.3, -58.1799}, {6.4, -52.3046}, \{6.5,
-46.5078}, {6.6, -40.827}, {6.7, -35.3016}, {6.8, -29.9653}, \{6.9,
-24.8465}, {7., -19.9717}, {7.1, -15.3617}, {7.2, -11.0341}, \{7.3,
-6.99813}, {7.4, -3.26171}, {7.5, 0.172043}, {7.6,
3.30803}, {7.7, 6.14966}, {7.8, 8.70572}, {7.9, 10.9888}, {8.,
13.0129}, {8.1, 14.7937}, {8.2, 16.3474}, {8.3, 17.6906}, {8.4,
18.8424}, {8.5, 19.8199}, {8.6, 20.6402}, {8.7, 21.3201}, {8.8,
21.8738}, {8.9, 22.317}, {9., 22.664}, {9.1, 22.926}, {9.2,
23.1148}, {9.3, 23.2406}, {9.4, 23.3121}, {9.5, 23.3539}, {9.6,
23.3247}, {9.7, 23.2789}, {9.8, 23.2081}, {9.9, 23.1102}, {10.,
22.9953}, {10.1, 22.866}, {10.2, 22.7242}, {10.3, 22.5727}, {10.4,
22.4149}, {10.5, 22.2485}, {10.6, 22.0785}, {10.7, 21.9067}, {10.8,
21.7264}, {10.9, 21.5564}, {11., 21.3797}, {11.1, 21.2037}, {11.2,
21.0281}, {11.3, 20.8535}, {11.4, 20.6802}, {11.5, 20.5083}, {11.6,
20.3377}, {11.7, 20.1697}, {11.8, 20.0034}, {11.9, 19.8403}, {12.,
19.6767}, {12.1, 19.5166}, {12.2, 19.3587}, {12.3, 19.2031}, {12.4,
19.0497}, {12.5, 18.8984}, {12.6, 18.7495}, {12.7, 18.6027}, {12.8,
18.4579}, {12.9, 18.3154}, {13., 18.1752}, {13.1, 18.0366}, {13.2,
17.9005}, {13.3, 17.7661}, {13.4, 17.6336}, {13.5, 17.5031}, {13.6,
17.3746}, {13.7, 17.2478}, {13.8, 17.1229}, {13.9, 16.9998}, {14.,
16.8767}, {14.1, 16.7583}, {14.2, 16.6403}, {14.3, 16.524}, {14.4,
16.4095}, {14.5, 16.2964}, {14.6, 16.1848}, {14.7, 16.0747}, {14.8,
15.966}, {14.9, 15.8598}, {15., 15.7531}, {15.1, 15.6488}, {15.2,
15.5469}, {15.3, 15.444}, {15.4, 15.3437}, {15.5, 15.2446}, {15.6,
15.147}, {15.7, 15.0505}, {15.8, 14.9559}, {15.9, 14.8611}, {16.,
14.7681}, {16.1, 14.6765}, {16.2, 14.5858}, {16.3, 14.4975}, {16.4,
14.4087}, {16.5, 14.3205}, {16.6, 14.2342}, {16.7, 14.149}, {16.8,
14.0647}, {16.9, 13.9818}, {17., 13.8992}, {17.1, 13.818}, {17.2,
13.7375}, {17.3, 13.6581}, {17.4, 13.5793}, {17.5, 13.5035}, {17.6,
13.4251}, {17.7, 13.3493}, {17.8, 13.2737}, {17.9, 13.2001}, {18.,
13.1268}, {18.1, 13.0542}, {18.2, 12.9826}, {18.3, 12.9122}, {18.4,
12.8414}, {18.5, 12.7719}, {18.6, 12.7034}, {18.7, 12.6354}, {18.8,
12.5681}, {18.9, 12.5015}, {19., 12.4358}, {19.1, 12.3707}, {19.2,
12.306}, {19.3, 12.2422}, {19.4, 12.1791}, {19.5, 12.1167}, {19.6,
12.0548}, {19.7, 11.9935}, {19.8, 11.9326}, {19.9, 11.873}, {20.,
11.8137}}
Which in turn can be plot, and I obtained this:
where y-coordinate is energy, and x-axis is distance. I have to find a value of distance for a given value of energy, and, as can be seen , for a given energy there can be several distances. For instance , I use an energy of y=18, which has, in fact, three corresponding distances, but I only can find one. I use interpolation first in the table and then use Solve but , I just obtained one value that is irrelevant for other calculations:
itb = Interpolation[tbff];
Solve[itb[z]==z]
{*z=0.0854959*}
Can anybody help me ? Thanks in advance.