The Visualization of the Space Probability Distribution for a Moving Particle: In a Single Ring-Shaped Coulomb Potential

<div>Relation between <svg height="9.25202pt" id="M188" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 11.7048 9.25202" width="11.7048pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z" id="g113-111"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.461,3.132)"><path d="M482 498C482 606 448 710 328 710C138 710 24 416 24 218C24 99 58 -12 184 -12C373 -12 482 294 482 498ZM395 521C395 483 391 449 383 395H128C158 537 226 671 312 671C388 671 395 566 395 521ZM375 342C348 190 284 25 192 25C128 25 109 116 109 199C109 243 112 292 121 342H375Z" id="g50-230"></path></g></svg> and <svg height="16.9324pt" id="M189" style="vertical-align:-5.341pt" version="1.1" viewbox="-0.0498162 -11.5914 26.9059 16.9324" width="26.9059pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M162 -163V703H101V-163H162Z" id="g113-9"></path></g><g transform="matrix(.013,0,0,-0.013,3.419,0)"><path d="M483 97L471 123C436 91 401 65 392 65C388 65 384 74 390 106C414 239 444 378 457 429L455 433C444 433 429 436 416 439C392 444 368 448 344 448C281 448 204 415 152 376C71 315 23 205 23 103C23 21 57 -12 85 -12C114 -12 149 6 185 34C231 70 285 119 329 183H331L309 81C292 0 308 -12 326 -12C350 -12 421 24 483 97ZM374 387C370 363 356 291 345 261C315 193 181 50 139 50C124 50 110 71 110 118C110 224 153 331 218 379C238 394 271 402 301 402C329 402 359 394 374 387Z" id="g113-98"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.412,3.132)"><path d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z" id="g50-111"></path></g><g transform="matrix(.0065,0,0,-0.0065,14.026,5.233)"><path d="M489 489C489 601 457 708 332 708C138 708 25 411 25 221C25 101 58 -12 189 -12C378 -12 489 294 489 489ZM400 519C400 480 398 450 388 397H132C162 535 231 665 316 665C391 665 400 562 400 519ZM378 339C354 187 285 28 196 28C132 28 114 119 114 202C114 243 115 290 126 339H378Z" id="g176-230"></path></g><g transform="matrix(.013,0,0,-0.013,18.393,0)"><path d="M162 -163V703H101V-163H162Z" id="g113-9"></path></g><g transform="matrix(.0091,0,0,-0.0091,21.812,-5.741)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path></g></svg> for different values <span class="nowrap"><svg height="9.49473pt" id="M190" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 6.21949 9.49473" width="6.21949pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M452 333C452 398 425 448 375 448C329 448 235 404 140 292H138L229 683C233 701 234 712 225 712C208 712 149 686 66 677L64 652H97C135 652 140 651 129 598L38 167C23 96 29 57 44 33C60 7 98 -12 132 -12C169 -12 232 3 290 41C383 102 452 223 452 333ZM365 316C365 199 308 87 239 49C221 39 200 35 183 35C137 35 99 70 112 163C116 191 123 215 129 233C190 316 290 392 330 392C348 392 365 372 365 316Z" id="g113-99"></path></g></svg>.</span></div>

Advances in High Energy Physics

fig1

Figure 1

Figure 1: The Visualization of the Space Probability Distribution for a Moving Particle: In a Single Ring-Shaped Coulomb Potential 